Question

The total number of ways in which 5 balls of different colors can be distributed among 3 persons so that each person gets at least one ball is:

• A. $75$
• B. $150$
• C. $210$
• D. $243$

Answer 1

Answer: (B)

$150$

'5' balls to be distributed among '3'.
Total number of distribution possible $=3\times 3\times .....5times$
$=3^5$.
Of these distributions, there are cases when one person does not get any ball.
Number of such cases
$={}^3{C}_1\times (2^5-2)$
$=90$
Also, there are cases when one gets all.
Number of such cases
$={}^3{C}_1=3$
So, distributions such that each gets at least 1 is
$3^5-90-3=243-93$
$=150$.