Question

The number of groups that can be made from $5$ different green balls, $4$ different blue balls and $3$ different red balls, if at least $1$ green and $1$ blue ball is to be included

• A. 3700
• B. 3720
• C. 4340
• D. None of these

Answer 1

Answer: (B)

At least one green ball can be selected out of $5$ green balls in $2^5-1,$ that is, in $31$ ways.
Similarly, at least one blue ball can be selected from 4 blue balls in $2^4-1=15$ ways.
And at least one red or not red can be select in $2^3=8$ ways.
Hence, required number of ways $=31\times 15\times 8=3720$