+9 Hey guys, I need some help :(
I have this question related about permutation and combination. Can you help me please? :<
The 4-digits numbers are 5352, 5114, 5818,..., have 2 common characteristics. First, they start with the digit 5. Second, exactly 2 digits in each numbers are identical. How many such numbers are there?
+26397 The 4-digits numbers are 5352, 5114, 5818,..., have 2 common characteristics. First, they start with the digit 5. Second, exactly 2 digits in each numbers are identical. How many such numbers are there?
1.500155.5131109.5262163.5405217.5520271.5597325.5744379.58752.500256.5133110.5265164.5411218.5521272.5598326.5745380.58773.500357.5135111.5266165.5414219.5523273.5600327.5747381.58784.500458.5141112.5272166.5415220.5524274.5605328.5750382.58805.500659.5144113.5275167.5422221.5526275.5606329.5751383.58816.500760.5145114.5277168.5424222.5527276.5611330.5752384.58827.500861.5150115.5282169.5425223.5528277.5615331.5753385.58838.500962.5152116.5285170.5433224.5529278.5616332.5754386.58849.501063.5153117.5288171.5434225.5530279.5622333.5756387.588610.501164.5154118.5292172.5435226.5531280.5625334.5758388.588711.501565.5156119.5295173.5440227.5532281.5626335.5759389.588912.502066.5157120.5299174.5441228.5534282.5633336.5765390.589513.502267.5158121.5300175.5442229.5536283.5635337.5766391.589814.502568.5159122.5303176.5443230.5537284.5636338.5767392.589915.503069.5161123.5305177.5446231.5538285.5644339.5770393.590016.503370.5165124.5311178.5447232.5539286.5645340.5771394.590517.503571.5166125.5313179.5448233.5540287.5646341.5772395.590918.504072.5171126.5315180.5449234.5541288.5650342.5773396.591119.504473.5175127.5322181.5450235.5542289.5651343.5774397.591520.504574.5177128.5323182.5451236.5543290.5652344.5776398.591921.505175.5181129.5325183.5452237.5546291.5653345.5778399.592222.505276.5185130.5330184.5453238.5547292.5654346.5779400.592523.505377.5188131.5331185.5456239.5548293.5657347.5785401.592924.505478.5191132.5332186.5457240.5549294.5658348.5787402.593325.505679.5195133.5334187.5458241.5560295.5659349.5788403.593526.505780.5199134.5336188.5459242.5561296.5660350.5795404.593927.505881.5200135.5337189.5464243.5562297.5661351.5797405.594428.505982.5202136.5338190.5465244.5563298.5662352.5799406.594529.506083.5205137.5339191.5466245.5564299.5663353.5800407.594930.506584.5211138.5343192.5474246.5567300.5664354.5805408.595031.506685.5212139.5344193.5475247.5568301.5667355.5808409.595132.507086.5215140.5345194.5477248.5569302.5668356.5811410.595233.507587.5220141.5350195.5484249.5570303.5669357.5815411.595334.507788.5221142.5351196.5485250.5571304.5675358.5818412.595435.508089.5223143.5352197.5488251.5572305.5676359.5822413.595636.508590.5224144.5354198.5494252.5573306.5677360.5825414.595737.508891.5226145.5356199.5495253.5574307.5685361.5828415.595838.509092.5227146.5357200.5499254.5576308.5686362.5833416.596539.509593.5228147.5358201.5501255.5578309.5688363.5835417.596640.509994.5229148.5359202.5502256.5579310.5695364.5838418.596941.510095.5232149.5363203.5503257.5580311.5696365.5844419.597542.510196.5233150.5365204.5504258.5581312.5699366.5845420.597743.510597.5235151.5366205.5506259.5582313.5700367.5848421.597944.511098.5242152.5373206.5507260.5583314.5705368.5850422.598545.511299.5244153.5375207.5508261.5584315.5707369.5851423.598846.5113100.5245154.5377208.5509262.5586316.5711370.5852424.598947.5114101.5250155.5383209.5510263.5587317.5715371.5853425.599048.5116102.5251156.5385210.5512264.5589318.5717372.5854426.599149.5117103.5253157.5388211.5513265.5590319.5722373.5856427.599250.5118104.5254158.5393212.5514266.5591320.5725374.5857428.599351.5119105.5256159.5395213.5516267.5592321.5727375.5859429.599452.5121106.5257160.5399214.5517268.5593322.5733376.5865430.599653.5122107.5258161.5400215.5518269.5594323.5735377.5866431.599754.5125108.5259162.5404216.5519270.5596324.5737378.5868432.5998
There are 432 such numbers
+26397 The 4-digits numbers are 5352, 5114, 5818,..., have 2 common characteristics. First, they start with the digit 5. Second, exactly 2 digits in each numbers are identical. How many such numbers are there?
1.500155.5131109.5262163.5405217.5520271.5597325.5744379.58752.500256.5133110.5265164.5411218.5521272.5598326.5745380.58773.500357.5135111.5266165.5414219.5523273.5600327.5747381.58784.500458.5141112.5272166.5415220.5524274.5605328.5750382.58805.500659.5144113.5275167.5422221.5526275.5606329.5751383.58816.500760.5145114.5277168.5424222.5527276.5611330.5752384.58827.500861.5150115.5282169.5425223.5528277.5615331.5753385.58838.500962.5152116.5285170.5433224.5529278.5616332.5754386.58849.501063.5153117.5288171.5434225.5530279.5622333.5756387.588610.501164.5154118.5292172.5435226.5531280.5625334.5758388.588711.501565.5156119.5295173.5440227.5532281.5626335.5759389.588912.502066.5157120.5299174.5441228.5534282.5633336.5765390.589513.502267.5158121.5300175.5442229.5536283.5635337.5766391.589814.502568.5159122.5303176.5443230.5537284.5636338.5767392.589915.503069.5161123.5305177.5446231.5538285.5644339.5770393.590016.503370.5165124.5311178.5447232.5539286.5645340.5771394.590517.503571.5166125.5313179.5448233.5540287.5646341.5772395.590918.504072.5171126.5315180.5449234.5541288.5650342.5773396.591119.504473.5175127.5322181.5450235.5542289.5651343.5774397.591520.504574.5177128.5323182.5451236.5543290.5652344.5776398.591921.505175.5181129.5325183.5452237.5546291.5653345.5778399.592222.505276.5185130.5330184.5453238.5547292.5654346.5779400.592523.505377.5188131.5331185.5456239.5548293.5657347.5785401.592924.505478.5191132.5332186.5457240.5549294.5658348.5787402.593325.505679.5195133.5334187.5458241.5560295.5659349.5788403.593526.505780.5199134.5336188.5459242.5561296.5660350.5795404.593927.505881.5200135.5337189.5464243.5562297.5661351.5797405.594428.505982.5202136.5338190.5465244.5563298.5662352.5799406.594529.506083.5205137.5339191.5466245.5564299.5663353.5800407.594930.506584.5211138.5343192.5474246.5567300.5664354.5805408.595031.506685.5212139.5344193.5475247.5568301.5667355.5808409.595132.507086.5215140.5345194.5477248.5569302.5668356.5811410.595233.507587.5220141.5350195.5484249.5570303.5669357.5815411.595334.507788.5221142.5351196.5485250.5571304.5675358.5818412.595435.508089.5223143.5352197.5488251.5572305.5676359.5822413.595636.508590.5224144.5354198.5494252.5573306.5677360.5825414.595737.508891.5226145.5356199.5495253.5574307.5685361.5828415.595838.509092.5227146.5357200.5499254.5576308.5686362.5833416.596539.509593.5228147.5358201.5501255.5578309.5688363.5835417.596640.509994.5229148.5359202.5502256.5579310.5695364.5838418.596941.510095.5232149.5363203.5503257.5580311.5696365.5844419.597542.510196.5233150.5365204.5504258.5581312.5699366.5845420.597743.510597.5235151.5366205.5506259.5582313.5700367.5848421.597944.511098.5242152.5373206.5507260.5583314.5705368.5850422.598545.511299.5244153.5375207.5508261.5584315.5707369.5851423.598846.5113100.5245154.5377208.5509262.5586316.5711370.5852424.598947.5114101.5250155.5383209.5510263.5587317.5715371.5853425.599048.5116102.5251156.5385210.5512264.5589318.5717372.5854426.599149.5117103.5253157.5388211.5513265.5590319.5722373.5856427.599250.5118104.5254158.5393212.5514266.5591320.5725374.5857428.599351.5119105.5256159.5395213.5516267.5592321.5727375.5859429.599452.5121106.5257160.5399214.5517268.5593322.5733376.5865430.599653.5122107.5258161.5400215.5518269.5594323.5735377.5866431.599754.5125108.5259162.5404216.5519270.5596324.5737378.5868432.5998
There are 432 such numbers
+118710 Thanks Heureka :)
Hey guys, I need some help :(
I have this question related about permutation and combination. Can you help me please? :<
The 4-digits numbers are 5352, 5114, 5818,..., have 2 common characteristics. First, they start with the digit 5. Second, exactly 2 digits in each numbers are identical. How many such numbers are there?
11(the third digit can be (0,2,3,4,6,7,8,9)
The third digit can be 1st 2nd or third so that it 8*3=24
There are 9 double digit possiblilities if you do not reuse 5 = 24*9=216 permutation.
Heureka's answer is different because he has allowed the 5 to be used once or twice.
So I would need to add all the ones with 2 fives.
9*8*3=216
216+216=432
Great, my answer is the same as Heureka's 
If you want more explanation then ask :)
+130491 We could have a second "5" in any one of three positions.......and for each of these, we have 9 choices for a digit to occupy one of the two remaining positions and 8 choices for the other...so.....
So C(3,1) * 9 * 8 = 216
Also, in the last three positions, excluding the digit "5,' we have the choice of the same digit occupying any 2 of 3 positions.......and there are 9 choices for these .......and the remaining position can be occupied by any of the 8 remaining digits.....so....
C(3,2)* 9 * 8 = 216
So 216 + 216 = 432
