Question -
Answer -
Given:
P (n – 1, 3): P (n, 4)= 1 : 9
P (n – 1, 3)/ P (n, 4)= 1 / 9
By using the formula,
P (n, r) = n!/(n – r)!
P (n – 1, 3) = (n –1)! / (n – 1 – 3)!
= (n – 1)! / (n – 4)!
P (n, 4) = n!/(n – 4)!
So, from the question,
P (n – 1, 3)/ P (n, 4)= 1 / 9
Substituting theobtained values in above expression we get,
[(n –1)! / (n – 4)!] / [n!/(n – 4)!] = 1/9
[(n –1)! / (n – 4)!] × [(n – 4)! / n!] = 1/9
(n – 1)!/n! = 1/9
(n – 1)!/n (n – 1)! =1/9
1/n = 1/9
n = 9
∴ The value of nis 9.