Question

Chetan goes to a toy store to buy $1$ ball-either a football, basket ball, or tennis ball and $3$ different board games. If the toy store is stocked with all types of balls but only $6$ different types of board games, how many different selections of $4$ items can he make consisting of $1$ type of ball and $3$ different board games?

• A. $18$
• B. $20$
• C. $54$
• D. $60$
• E. $162$

Answer 1

The correct option is D $60$

• He can select one ball from any three of types in ${{}^{3}C}_1=3$ ways
• He can select three different board games from 6 different types in ${{}^{6}C}_3=20$ ways
• So the total number of possibilities of selecting $1$ ball and $3$ board games is $3\times 20=60$