Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If α is the number of oneone functions from X to Y and β is the number of onto functions from Y to X , then the value of 1/5!(β-α) is \ \ \ \ \ \ .

Mathematics · Functions

JEE Advanced 2018 — Paper 2 — Question 36

Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If $\alpha$ is the number of oneone functions from $X$ to $Y$ and $\beta$ is the number of onto functions from $Y$ to $X$ , then the value of $\frac{1}{5!}(\beta-\alpha)$ is $\_\_\_\_\_\_$ .

Answer: 119

Numerical answer — enter this value.

Step-by-step solution

$\alpha={ }^{7} \mathrm{C}_{5} \cdot 5!=2520$

\begin{aligned} & \beta=5^{7}-{ }^{5} \mathrm{C}_{1} 4^{7}+{ }^{5} \mathrm{C}_{2} 3^{7}-{ }^{5} \mathrm{C}_{3} 2^{7}+{ }^{5} \mathrm{C}_{4}=16800 \\& \frac{\beta-\alpha}{5!}=119 \end{aligned}

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Exam: JEE Advanced 2018
Paper: Paper 2
Subject: Mathematics
Chapter: Functions
Topic: One-One, many-one, onto, into, bijective functions

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Answer: 119

Step-by-step solution

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