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Question

Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If α is the number of one-one functions from X to Y and β is the number of onto functions from Y to X, then the value of 15!(βα) is _______.

Solution
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n(X)=5
n(Y)=7
α Number of one-one function =7C5×5!
β Number of onto function Y to X
1,1,1,1,3 1,1,1,2,2
7!3!4!×5!+7!(2!)33!×5!=(7C3+3.7C3)5!=4×7C3×5!
βα5!=4×7C37C5=4×3521=119.
827605_903739_ans_4b4bb21fbb104219978b570902959755.png

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