Question

In how many ways the letters of the word crisis be arranged

Answer 1

There are 6 letter in the word crisis so the answer seems to be 6! (6 factorial), but there are two 'i's and two 's's which are indistinguishable and each of which can be arranged in 2! ways. So:

number_of_ways = 6!/2!2!

= 180 ways.

Answer 2

Given,

The word CRISIS

To find,

Number of ways the word crisis can be arranged.

Solution,

Now, we have the word CRISIS.

This word has

C = one time (1C)

R = one time(1R)

I = two time(2I's)

S = two time(2S's)

Word CRISIS has 6 letters in total.

Number of ways the letters of the word CRISIS can be arranged = $\frac{6!}{1!1!2!2!}$

= $\frac{6*5*4*3}{2}$

= 6 x 5 x 2 x 3

= 180

Hence, number of ways the letters of the word crisis be arranged is 180.