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  4. 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

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Q. 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

Permutations and Combinations

Solution:

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 $=31 \times 15 \times 8=3720$