SATHEE: Permutations and Combinations 4 Question 4

Permutations and Combinations 4 Question 4

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

(2012)

(a) 75

(b) 150

(d) 243

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Answer:

Correct Answer: 4. (b)

Solution:

Objects

Distinct

Groups

Objects

Identical

Groups

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 1 : A=1, B=1, c=2

case 2 : A=1, B=2, c=2

Number of ways to distribute 5 balls

$\begin{aligned} =^{5} C_{1} \cdot^{4} C_{1} \cdot^{3} C_{3} \times \frac{3!}{2!} +^{5} C_{1} \cdot^{4} C_{2} \cdot^{2} C_{2} \times \frac{3!}{2!} \\ = 60 + 90 = 150 \end{aligned}$

Permutations and Combinations 4 Question 4

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

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Permutations and Combinations 4 Question 4

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

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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