In a shop there are five types of ice-creams available. A child buys six ice-creams. Statement -1: The…

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 ${ }^{10} \mathrm{C}_5$. 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 $6 \mathrm{~A}^{\text {'s }}$ and 4 B's in a row.
  1. Statement $-1$ is false, Statement $-2$ is true
  2. Statement $-1$ is true, Statement $-2$ is true, Statement $-2$ is a correct explanation for Statement $-1$
  3. Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is not a correct explanation for Statement $-1$.
  4. Statement $-1$ is true, Statement $-2$ is false.

Solution

$ \begin{aligned} & x_1+x_2+x_3+x_4+x_5=6 \\ & 5+6-1 C_{5-1}={ }^{10} C_4 \end{aligned} $

Asked in: JEE Main 2008

Practice more Permutation Combination questions on Aicharya