Question

21. A cycle of length n can be
expressed as the product of :
(A) n-1 permutations
(B) n permutations
(C) n+1 permutations
(D) None​

Answer 1

(A) n-1 permutations

Step-by-step explanation:

Given

A cycle of length n can be expressed

Step : 1(i)

assume the value

a cycle length = n,

permutations = p

Step : 1(ii)

formula of permutations is P= n/(n-r)

P = permutation

n= total number of objects

r = number of objects selected

Step : 1(iii)

To Find: cycle length n,

apply the values and find the cycle length

P=n/(n-r)

here, r=1 (number of object is one cycle only)

P=n/(n-1)

(n-1) P=n

therefore, n=(n-1) P (P=permutation)

A cycle of length n is n-1 permutations is solved