Question

Statement-1 : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is ⁹C₃.
Statement-2 : The number of ways of choosing any 3 places from 9 different places is ⁹C₃.
(a) Statement-1 is true, Statement-2 is false.
(b) Statement-1 is false, Statement-2 is true.
(c) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(d) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

Answer 1

(c) : x₁ + x₂ + x₃ + x₄ = 10
The number of positive integral solution is
^{6 + 4 – 1}C_{4 – 1} = ⁹C₃
It is the same as the number of ways of choosing any 3 balls from 9 different places.