Verified Solution • 2025–26 Session moderate

QJEEM08Ma5c58: JEE Main 2008 Mathematics - Class 11 JEEM08Ma5c58 Solution: In a shop there are five types of ice-cream available. A child…

In a shop there are five types of ice-cream available. A child buys six ice-cream.
Statement - 1: The number of different ways the child can buy the six ice-cream is 10C5.
Statement - 2: The number of different ways the child can buy the six ice-cream is equal to the number of different ways of arranging 6 A and 4 B's in a row.

Multiple Choice Options

  • 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

Step-by-Step Verified Solution

Note : n items can be distribute among p persons are n+p−1Cp−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.

∴ The number of different ways the child can buy the six ice-cream is = 6+5−1C5−1 = 10C4

∴ Statement - 1 is false.

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

= 10!6!4!=10C4

∴ Statement - 2 is true.

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