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 6A’s and 4B’s is a row 

The given situation in statement 1 is equivalent to find the non negative integral solutions of the equation  . Which is coeff, of  x⁶ in the expansion of

$\therefore$  Statement 1 is wrong.
Number of ways of arranging 6A’s and 4B’s in a row 
$=\frac{10}{6!4!}$$={}^{10}C_5$  which is same as the number of ways the child can buy six icecreams.
$\therefore$ Statement 2 is true