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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 → Y and β is the number of onto functions from Y → X , then the value of 1 5 ! β - α is _____-.

Correct answer

0

Step-by-step solution

n X = 5 n Y = 7 α → Number of one-one function = 7 C 5 × 5 ! β → Number of onto function Y to X So, β = 7 ! 3 ! 4 ! × 5 ! + 7 ! 2 ! 3 3 ! × 5 ! = 7 C 3 + 3 . 7 C 3 5 ! = 4 × 7 C 3 × 5 ! β - α 5 ! = 4 × 7 C 3 - 7 C 5 = 4 × 35 - 21 = 119

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