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.

Engineering

Mathematics

Permutation and Combination Basic Definitions

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.

Statement-1 is true, Statement-2 is false

Statement-1 is false, Statement-2 is true.

Statement-1 is true, Statement-2 is true and Statement-2 is the correct explanation of Statement-1.

Statement-1 is true, Statement-2 is false and Statement-2 is not the correct explanation of Statement-1

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Statement - 1 :

B₁ + B₂ + B₃ + B₄ = 10

= coefficient of x¹⁰ in (x¹ + x² + .....+ x⁷)⁴

= coefficient of x⁶ in (1 – x⁷)4 (1 – x)^–4

= ⁴⁺⁶^–1C₆ = ⁹C₃

Statement - 2 :

Obviously ⁹C₃