Question

np5+5.np4=10pr find r

Answer 1

Answer:

n = 9 , r = 5

Step-by-step explanation:

nPr = n!/ [ n - r ] !

please solve using this formula

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Answer 2

Answer:

5

Step-by-step explanation:

We know that nPr = n!/ [ n - r ] !

np5 = n!/[n-5]!

5*np4 = 5*n!/[n-4]!

n!/[n-5]! + 5*n!/[n-4]! = 10!/[10-r]!

n!/[n-5]! + 5*n!/[n-4][n-5]! = 10!/[10-r]!

n!/[n-5]! {1 + 5/[n-4]} = 10!/[10-r]!

n!/[n-5]! {[n-4]+ 5/n-4} = 10!/[10-r]!

n!/[n-5]! {n+1/n-4} = 10!/[10-r]!

[n+1]!/[n-4]! = 10!/[10-r]!

In numerator,

n+1 = 10

n = 10-1

n = 9

In denominator, substituting the value of n

[n-4] = [10-r]

[9-4] = [10-r]

5 = 10-r

5-10 = -r

-5 = -r

5 = r