Question

A bag contains $3$ black, $4$ white and $2$ red balls, all the balls being different. The number of selections of at most 6 balls containing balls of all the colors is

• A. $42(4!)$
• B. $270$
• C. $(2^6-1)(4!)$
• D. none of these

Answer 1

The correct option is A $42(4!)$

Required number of selection
${=}^3{C}_1{\times }^4{C}_1{\times }^2{C}_1\left({}^6{C}_3{+}^6{C}_2{+}^6{C}_1{+}^6{C}_0\right)=3\times 4\times 2(20+15+6+1)=42(4!)$