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 - Mathematics MCQ AIEEE 2026 | ExamTest.live | ExamTest.live

Home Tests Search Rank Profile

mediumMCQAIEEE2026Mathematics

1 mark

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.

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 & Step-by-step Explanation

This is a problem of selecting r items from n types with replacement. n = 5 (types), r = 6 (items to buy).Number of ways =^{n + r - 1} C_{r} =^{5 + 6 - 1} C_{6} =^{10} C_{6} =^{10} C_{4} .Statement 1 says^{10} C_{5}, which is false.Statement 2: Arranging 6 A’s and 4 B’s (total 10 items) in a row is \frac{10 !}{6 ! 4 !} =^{10} C_{4} or^{10} C_{6} .This matches the correct calculation. So Statement 2 is true.

Practice this question

Try it yourself before checking the explanation above.

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.

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

Share This Question

permutations and combinations

Related Questions

Which one of the following statements is true?

Which of the following statements is not correct?

Which one of the following statements is correct?

The product formed by the reaction of an aldehyde with a primary amine is:

Which part of the tobacco plant is infected by Meloidogyne incognita?

The term ecosystem was coined by:

Ready for a Full Test?

Practice with timed mock tests and track your performance across Mathematics.

Browse Tests Leaderboard

Discussion