In a shop there are five types of ice-creams available.

Question

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.

Accepted Answer

Note : n items can be distribute among p persons are ${}^{n + p - 1}{C_{p - 1}}$ ways.

Here n = 6 ice-cream

p = 5 types of ice-cream

Each ice-cream belongs to one of the 5 ice-cream type. So chosen 6 ice-crean can be divide into 5 types of ice-cream.

$$ \therefore $$ The number of different ways the child can buy the six ice-cream is = ${}^{6 + 5 - 1}{C_{5 - 1}}$ = ${}^{10}{C_4}$

$$ \therefore $$ Statement - 1 is false.

Number of different ways of arranging 6 A and 4 B's in a row

= $${{10!} \over {6!4!}} = {}^{10}{C_4}$$

$$ \therefore $$ Statement - 2 is true.

Solutions · 1