Question

how many distinguishable permutations of letters are possible using the letters in the word maryland?

A. 20,160

B. 5,040

C. 40,320

D. 80,640

Answer 1

If there are "n" objects, with n₁ of a first type, n₂ of a second type, n₃ of a third type, n_r of a r^th type,

where n₁ + n₂ + n₃ + .... n_r = n there there will be

n! / ( n₁! * n₂! * n₃! * .....n_r! ) linear arrangements or permutations of the objects since the objects are indistinguishable

Here the word is maryland

Number of m's = 1

Number of a's = 2

Number of r's = 1

Number of y's = 1

Number of l's = 1

Number of n's = 1

number of d's = 1

Number of total letters = 8

So total number of permutations = 8! / ( (1!)⁷ * 2! )

= 8! / 2!

= 40320 / 2

= 20160

So Answer is Option A