Question

How many arrangements can be made with the letters of the word 'SERIES'? How many of these begin and end with 'S' ? ​

Answer 1

Answer:

The total number of ways are 180. Out of which 12 starts and ends with 'S'.

Step-by-step explanation:

Consider the provided word 'SERIES'

There are 6 letters. So the possible arrangements can be: 6!

But if we observe the word 'SERIES' we can find that the letter S and E comes 2 times, so to find the total number of arrangements we will divide 6! by 2! times 2!.

$\frac{6!}{2!\times 2!}=\frac{2!\times 3\times 4\times 5\times 6}{2!\times2}$

$\frac{6!}{2!\times 2!}=3\times 2\times 5\times 6$

$\frac{6!}{2!\times 2!}=180$

Hence, the total number of ways are 180.

Now find how many of these begin and end with S.

If we fixed the letter S in the end and begin, we will only left with 4 letters. i.e ERIE

But out of these 4 letters E comes 2 times.

So, the number of arrangements can be calculated as:

$\frac{4!}{2!}=12$

Hence, 12 arrangements can be made begin and end with 'S'.

Answer 2

Step-by-step explanation:

S E R I E S

All possible arrangements :

6!/2!*2! = 6*5*4*3/2 = 180

4!/2! = 12 begin & end with S