First slide

Permutations

Question

If $^{12} P_{r} =^{11} P_{6} + 6 \cdot^{11} P_{5}$ then r is equal to

Moderate

A

6
B

5
C

7
D

none of these

Solution

We know that
$r \cdot^{n - 1} {p_{r - 1} +}^{n - 1} p_{r =^{11} p_{r}}$
$∴$ $6 \cdot^{11} P_{5} +^{11} P_{6} =^{12} P_{6}$ $[Putting r = 6, n = 12]$
$=^{12} P_{r} =^{12} P_{6} \Rightarrow r = 6 [∵ 6 \cdot^{11} P_{5} +^{11} P_{6} =^{12} P_{r} (given)!$

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