Question

If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is ______.

Options

• `965/2^11`

• `965/2^10`

• `945/2^10`

• `945/2^11`

Answer 1

If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is `underlinebb(945/2^10)`.

Explanation:

Total number of ways to place 10 different balls in 4 distinct boxes = 4¹⁰

Required probability

= `(""^4"C"_2xx""^10"C"_2xx""^8"C"_3xx2^5xx2!)/4^10`

= `((4xx3)/2xx(10xx9)/2xx(8xx7xx12)/6xx2^5xx2)/2^20`

= `(6xx45xx56xx2)/2^15`

= `(2xx3xx45xx8xx7xx2)/2^15`

= `(3xx45xx7)/2^10`

= `945/2^10`