Number of groups that can be made from 5 different green balls, 4 different blue balls and 3 differe

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Gujarati

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6.Permutation and Combination

hard

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

(IIT-1974)

Solution

(b) At least one green ball can be selected out of $5$ green balls in ${2^5} – 1$

$i.e.$, 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 = $31 \times 15 \times 8 = 3720$.

Standard 11

Mathematics

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