Question

find the number of ways of arranging the letters of the word singing​

Answer 1

630 of ways of arranging the letters of the word SINGING.

How to find the number of ways of arranging :

• In word SINGING, there are 2I,2N,2G and 1S.

• Total no. of letters = 7

• Since letters are repeating, thus,

• Total no. of arrangements =  $\frac{7!}{2!X2!X2!}$

​                                             ⇒ $7!=7 X 6X5X4X3X2X1$

                                            ⇒ $2!=2X1$

                                            ⇒ $\frac{7 X 6X5X4X3X2X1}{2X1X2X1X2X1}$

                                            ⇒ $630$

630 of ways of arranging the letters of the word SINGING.

Answer 2

Answer:

The number of ways of arranging the letters of the word singing is​ 630.

Step-by-step explanation:

Given: A word is singing​.

We have to write a number of ways of arranging the letters of the word singing​.

We are solving in the following way:

We have,

A word is singing​.

First, we will arrange the above word in alphabetical order.

ggiinns

Here, we can see that g, i, and n come 2 times.

So, the number of ways of arranging the letters of the word singing​ will be:

$=>\frac{7!}{2!2!2!}\\\\=>\frac{7\times6\times5\times4\times3\times2\times1}{2\times1\times2\times1\times2\times1} \\\\=>\frac{5040}{8} \\\\=>630$

Hence, the number of ways of arranging the letters of the word singing is​ 630.