A boy needs to select five courses from 12 available courses, out of which 5 courses are language co

English

Gujarati

Hindi

6.Permutation and Combination

medium

A boy needs to select five courses from $12$ available courses, out of which $5$ courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is

A

$454$

B

$465$

C

$546$

D

$645$

(JEE MAIN-2023)

Solution

For at most two language courses

$={ }^5 C _2 \times{ }^7 C _3+{ }^5 C _1 \times{ }^7 C _4+{ }^7 C _5=546$

Standard 11

Mathematics

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