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Let X be the set with exactly 5 elements and Y be the 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 151(β-α)=

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answer is 119.

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Detailed Solution

Given nX=5 and nY=7α→ Number of one-one function =C5   7×5! The number of onto functions from Y to X is β =7!3!4!×5!+7!(2!)33!×5!=C3   7+3xC3   75!=4×C3   7×5!β-α51=4×C3   7-C5   7=4×35-21=119
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Let X be the set with exactly 5 elements and Y be the 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 151(β-α)=