Question Detail

STA 112 PERMUTATIONS AND COMBINATIONS Objective Question
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Question

If 12C5 + 12C6 = XC6, then what is the value of X?
Options
A 12
B 13
Correct Answer
C 14
D 15
Correct Answer

Option B is the correct answer.

Detailed Explanation

This problem uses Pascal's Identity for combinations, which states that nCr + nCr+1 = n+1Cr+1. Comparing this identity to the given equation 12C5 + 12C6 = XC6, we can see that n = 12 and r = 5. Therefore, 12C5 + 12C6 = 12+1C5+1 = 13C6. Thus, X = 13.

Hint

Apply Pascal's Identity for combinations: nCr + nCr+1 = n+1Cr+1.

Question Info

Course: STA 112
Topic: PERMUTATIONS AND COMBINATIONS
Type: Objective
Difficulty: Not specified
Question 73 of 112
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