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The total number of ways in which 5 ball...

The total number of ways in which 5 balls of differert colours can be distributed among 3 persons so thai each person gets at least one ball is

A

75

B

150

C

210

D

243

Text Solution

Verified by Experts

The correct Answer is:
B
`{:("Objects", "Groups", "Objects", "Groups"),("Distinct", "Distinct", "Identical", "Identical"),("Distinct", "Identical", "Identical", "Distinct"):}`
Description of Situation Here, 5 distinct balls are distributed amongst 3 persons so that each gets at least one ball. i.e. `"Distinct " to " Distinct"`
So, we should make cases
`"Case I " {:(A, B, C),(1, 1, 2):}} " ""Case II " {:(A, B, C),(1, 2, 2):}}`
Number of ways to distribute 5 balls
`= (""^(5)C_(1) * ""^(4)C_(1) * ""^(3)C_(3) xx (3!)/(2!)) + (""^(5)C_(1) * ""^(4)C_(2) * ""^(2)C_(2) xx (3!)/(2!))`
`= 60 + 90 = 150`
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