Question

Find n if nP4
= 10 * nP3
.

Answer 1

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Answer 2

Answer:    

nP4=10× nP3

⇒n = 13

Explanation:  

permutation formula :

nPr = factorial of  n / factorial of  (n-1)

we have to use this formula for finding the value of n .  

solve:

nP4 = 10× nP3

⇒fact n/ fact (n-4) = 10×[fact n/ fact (n-3)]  

⇒1/ fact (n-4) = 10 × [ 1/ fact (n-3) ]

⇒1/ fact (n-4) = 10× [ 1/ {fact (n-4)  × n-3} ]

⇒1 = 10/ (n-3)

⇒n-3 = 10

⇒ n= 10+3 = 13

so, the value of n is 13.