Question

A box contains $7$ red, $6$ white and $4$ blue balls. In how many ways can a selection of $3$ balls be made,if none of the balls selected should be red?

• A. $135$
• B. $64$
• C. $50$
• D. $120$

Answer 1

The correct option is D $120$

$7$ Red , $6$ White , $4$ Blue

None of them should be red

Selecting $3$ balls

${\Rightarrow }^6{C}_3{+}^4{C}_3{+}^6{C}_2^4{C}_1{+}^6{C}_1^4{C}_2=20+4+15\left(4\right)+6\left(6\right)=24+60+36=120$

Therefore number of possiblities $=120$