In how many distinct ways can the letters of the word \text{KADUNA} be arranged? — JAMB UTME

In how many distinct ways can the letters of the word $\text{KADUNA}$ be arranged?

The total number of distinct arrangements is

360

The word

\text{KADUNA}

consists of

6

total letters with the letter '\text{A}' repeated

2

times. Using the formula for permutations with identical items, the number of distinct arrangements is

\frac{6!}{2!} = \frac{720}{2} = 360

Count the total number of letters in the word

\text{KADUNA}

and identify repetitions.

Total letters

n = 6

. The letter '\text{A}' appears

2

times, while '\text{K}', '\text{D}', '\text{U}', and '\text{N}' each appear

1

time.

Arrangements of

n

items with repeated elements require dividing

n!

by the factorial of the count of each repeated element.

Apply the permutation formula for repeated elements:

P = \frac{n!}{p!}

where

p

is the frequency of the repeated letter.

P = \frac{6!}{2!} = \frac{720}{2} = 360

Dividing by

2!

eliminates duplicate arrangements caused by swapping identical letters.

Permutations of items with repeated elements

Estimated Time:45s

Question