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# Counting

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Using the digits 2, 3, 4, 7 and 8, Carlos will form five-digit positive integers. Only the digits 2 and 3 can be used more than once in any of Carlos’ five-digit integers. How many distinct fivedigit positive integers are possible?

Jan 11, 2022

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1 - (22222, 22223, 22224, 22227, 22228, 22233, 1 22234, 22237, 22238, 22247, 22248, 22278, 22333, 22334, 22337, 22338, 22347, 22348, 22378, 22478, 23333, 23334, 23337, 23338, 23347, 23348, 23378, 23478, 33333, 33334, 33337, 33338, 33347, 33348, 33378, 33478)==36 combinations.

2 - Convert the above 36 combination to permutations as follows:
22222 ( 1 ) , 22223 ( 5 ) , 22224 ( 5 ) , 22227 ( 5 ) , 22228 ( 5 ) , 22233 ( 10 ) , 22234 ( 20 ) , 22237 ( 20 ) , 22238 ( 20 ) , 22247 ( 20 ) , 22248 ( 20 ) , 22278 ( 20 ) , 22333 ( 10 ) , 22334 ( 30 ) , 22337 ( 30 ) , 22338 ( 30 ) , 22347 ( 60 ) , 22348 ( 60 ) , 22378 ( 60 ) , 22478 ( 60 ) , 23333 ( 5 ) , 23334 ( 20 ) , 23337 ( 20 ) , 23338 ( 20 ) , 23347 ( 60 ) , 23348 ( 60 ) , 23378 ( 60 ) , 23478 ( 120 ) , 33333 ( 1 ) , 33334 ( 5 ) , 33337 ( 5 ) , 33338 ( 5 ) , 33347 ( 20 ) , 33348 ( 20 ) , 33378 ( 20 ) , 33478 ( 60 ) , >>Total combinations = 36
>>Total permutations = 992 [The numbers in brackets are the number of permutations for each combination.]

Jan 12, 2022