Q56 / 105 · JEE Main 2008 · Mathematics

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.

  • Correct answer
    A
    Statement $-1$ is false, Statement $-2$ is true
  • B
    Statement $-1$ is true, Statement $-2$ is true, Statement $-2$ is a correct explanation for Statement $-1$
  • C
    Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is not a correct explanation for Statement $-1$.
  • D
    Statement $-1$ is true, Statement $-2$ is false.

Solution

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

Hence, the correct answer is option: 'A'.

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