Question Detail

STA 112 PERMUTATIONS AND COMBINATIONS Objective Question
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Question

Given that 12C5 = 12Cr, and r ≠ 5, what is the value of r?
Options
A 12
B 7
Correct Answer
C 5
D 0
Correct Answer

Option B is the correct answer.

Detailed Explanation

A property of combinations states that if nCa = nCb, then either a = b or a + b = n.Given 12C5 = 12Cr.Case 1: r = 5. However, the problem states r ≠ 5.Case 2: r + 5 = 12r = 12 - 5r = 7.Therefore, the value of r is 7.

Hint

Apply the property of combinations nCr = nC(n-r).

Question Info

Course: STA 112
Topic: PERMUTATIONS AND COMBINATIONS
Type: Objective
Difficulty: Not specified
Question 97 of 112
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