Question

Ravi has five friends. In how many ways can he invite one or more for a dinner?

• A. 32
• B. 31
• C. 25
• D. 120

Answer 1

The correct option is B 31

The question is about selecting 1 or more things from 5 different things.

He can select one in ${}^5{C}_1$ ways

He can select two in ${}^5{C}_2$ ways

....

He can select all five in ${}^5{C}_5$ ways.

Hence total no. of ways = ${}^5{C}_1$ + ${}^5{C}_2$ + ${}^5{C}_3$ + ${}^5{C}_4$ + ${}^5{C}_5$ = $2^5$ – 1 = 31.