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Question

Assertion :If a,b,c are positive integers such that a+b+c8 , then the number of possible values of the ordered triplets (a,b,c) is 56. Reason: The number of ways in which n distinct things can be distributed among r girls such that each get at least one is n1Cn

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

The correct option is C Assertion is correct but Reason is incorrect
Consider a+b+c8
The number of possible ordered triplets is
=8P(31)
=8P2
=8!6!
=56.
Consider the reason,
Now n1Cn is not possible as n1<n and (n)! is not defined for any natural number n.
For nCr nr and n,r0
Hence the reason is false.

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