If 10 different balls are to be placed in 4 distinct boxes at...

Total number of ways in which 10 balls can be placed in 4 boxes =$4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4$

$⇒ {4}^{10}$

$⇒ {2}^{20}$

Exactly two box contain $2, 3$ balls

$⇒ C2 4 \times 2 \times C2 10 \times C3 8 \times {2}^{5}$

Probability $= \dfrac{C2 4 \times 2 \times C2 10 \times C2 8 \times {2}^{5}}{{2}^{20}}$

$= \dfrac{945}{{2}^{10}}$