Let P n denotes the number of ways of selecting 3 people out of ' n ' sitting in a row , if no two of them are consecutive and Q n is the corresponding figure when they are in a circle. If P n − Q n = 6, then ' n ' is equal to:
Text Solution
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(10)
Sol. Here ; P n = 
∴ x 1 + x 2 + x 3 + x 4 = n – 3 ∴ x 1 , x 4 ≥ 0
∴ x 1 + y 2 + y 3 + x 4 ≥ n – 5 x 2 , x 3 ≥ 1
p n = n – 5 + 4 – 1 c 3 = n – 2 c 3 y 2 , y 3 ≥ 0
Q n = 
∴ x 1 + x 2 + x 3 = n – 3 ⇒ y 1 + y 2 + y 3 = n – 6
Now P n – Q n = 6
= 6 ⇒ n = 10
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