NIMCET 2020 — Mathematics PYQ

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Question

NIMCET 2020 — Mathematics PYQ

NIMCET | Mathematics | 2020

6 Naresh has 10 friends, and he wants to invite 6 of them to a party. How many times will 3 particular friends never attend the party?

Choose the correct answer:

Explanation

Concept:
$^{n} C_{r} = \frac{n !}{r ! ( n - r )!}$
Calculations:
Given, Naresh has 10 friends, and he wants to invite 6 of them to a party.
Remove the 3 particular friends and invite 6 friends from the remaining = 10 - 3 = 7 friends.
This can be done in $^{7} C_{6}$ ways
Hence, required number of ways = $^{7} C_{6}$
$\Rightarrow$ required number of ways $= \frac{7 !}{( 7 - 6 )! 6 !}$
$\Rightarrow$ required number of ways $= 7$
Hence, Naresh has 10 friends, and he wants to invite 6 of them to a party. total number of ways that 3 particular friends never
attend the party = 7