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?

Concept:

\(\rm ^nC_r = \dfrac{n!}{r!(n-r)!}\)

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 ⁷C₆ ways
 

Hence, required number of ways = 7C6 

⇒required number of ways = \(\rm \dfrac{7!}{(7-6)!6!}\)

⇒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