Maths · Simple applications
Assertion In the shop there are five types of ice- creams available, a child buy
Assertion In the shop there are five types of ice- creams available, a child buys six ice- creams. Reason The number of different ways the child can buy the six ice-creams is \( ^{10} C_{3} \)
- A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
- B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
- C. Assertion is correct but Reason is incorrect
- D. Both Assertion and Reason are incorrect
Step-by-step solution
The assertion is a factual statement: there are five types of ice-cream and a child buys six. This is not claimed to be a problem, just a scenario. The reason provides an incorrect formula for the number of ways to buy six ice-creams from five types with repetition allowed. The correct count is C(5+6-1, 6) = C(10,6) = C(10,4) = 210, not C(10,3) = 120. Hence assertion is correct but reason is incorrect.
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