| In a shop there are five types of ice-creams available. A child buys six ice-creams. |
| Statement-1: The number of different ways the child can buy the six ice-creams is \[^{10}{{C}_{5}}\]. |
| Statement-2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A"s and 4 B"s in a row. |
A) Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.
B) Statement-1 is true, Statement-2 is false.
C) Statement-1 is false, Statement-2 is true.
D) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for = Statement-1.
Correct Answer: C
Solution :
Statement-1: Number of ways = number of non negative integral solutions of the equation \[{{T}_{1}}+{{T}_{2}}+T{{}_{3}}+{{T}_{4}}+{{T}_{5}}+T=6\] \[{{=}^{6+5-1}}{{C}_{5-1}}{{=}^{10}}{{C}_{4}}\] \[\therefore \] Statement-1 is wrong. Statement-2: Number of different ways of arranging 6A?s and 4 B?s in a row \[=\frac{10!}{6!4!}{{=}^{10}}{{C}_{4}}\] \[\therefore \] Statement-2 is correct.
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