Question

10 apples are distributed at random among 6 persons. The

probability that at least one of them will receive none, is -

• A. $\frac { 6 } { 143 }$
• B. $\frac { { } ^ { 14 } \mathrm { C } _ { 4 } } { { } ^ { 15 } \mathrm { C } _ { 5 } }$
• C. $\frac { 137 } { 143 }$
• D. None of these

Answer 1

Answer: (C)

$\frac { 137 } { 143 }$

Answer 2

The required probability

= 1 – probability of each receiving at least one

= 1 – .

Now, the number of integral solutions of

x₁ + x₂ + x₃ + x₄ + x₅ + x₆ = 10

such that x₁ ³ 1, x₂ ³ 1, ……, x₆ ³ 1 gives n(5) and the number of integral solutions of x₁ + x₂ + …. + x₅ + x₆ = 10 such that x₁ ³ 0, x₂ ³ 0, ….. , x₆ ³ 0 gives n(S).

\ the required probability = 1 – $\frac { { } ^ { 10 - 1 } C _ { 6 - 1 } } { { } ^ { 10 + 6 - 1 } C _ { 6 - 1 } }$

= 1 – $\frac { { } ^ { 9 } \mathrm { C } _ { 5 } } { { } ^ { 15 } \mathrm { C } _ { 5 } }$ = $\frac { 137 } { 143 }$ .

Hence (3) is the correct answer