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Determine the average of all four digit numbers that can be made using all the digits 2, 3, 5, 7 and 11 exactly once?

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Determine the average of all four digit numbers that can be made using all the digits 2, 3, 5, 7 and 11 exactly once?

(a) 3993

(b) 1555

(c) 5486

(d) 1347

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The above asked question is from Counting topic in division Counting of Discrete Mathematics

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Right choice is (b) 1555

Explanation: First we need to find the sum of all possible numbers and then divide it by the total such numbers possible to gain an average of all the numbers. So, we have (n-1)!(sum of digits)(1111…n times)/n!. Here n = 4. Therefore, (5-1)!(2+3+5+7+11)(1111)/5! = 1555.

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