Question

Find the number of ways the letters of the word ‘RUBBER can be arranged​

Answer 1

Answer:

total 6 laters so

6*5*4*3*2*1=720

Answer 2

Given,

The word RUBBER

To find,

Number of ways the letters of the word ‘RUBBER can be arranged​.

Solution,

We can use permutations and combinations concept in order to solve these questions.

In this question, the word RUBBER has 6 letters in it.

Let us take total letters as N = 6.

R,U,B,B,E,R are the letters.

R is repeated twice. (2Rs)

U is repeated once. (1 U)

B is repeated twice. (2 B's)

E is repeated once. (1 E)

Number of ways the letters can be arranged = $\frac{N!}{(2R!)(U!)(2B!)(E!)}$

= $\frac{6!}{(2*1!)(1!)(2*1)!(1!)}$

Now, solve it further ,

=  6 × 5 × 3 × 2

= 180

Hence, the number of ways the letters of the word 'RUBBER' can be arranged is 180.