Question Detail

STA 112 PERMUTATIONS AND COMBINATIONS Objective Question
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Question

What is the value of x, if 12C5 + 12C6 = XC6?
Options
A 11
B 12
C 13
Correct Answer
D 14
Correct Answer

Option C is the correct answer.

Detailed Explanation

This question uses Pascal's Identity for combinations, which states: nCr + nCr+1 = n+1C(r+1).Here, n = 12 and r = 5.So, 12C5 + 12C6 = (12+1)C(5+1) = 13C6.Comparing this to XC6, we find that X = 13.

Hint

Recall 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 109 of 112
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