Question

In rearranging the letters of a word such as KETCHUP, the number of possiblities for the first letter is seven because any one of the seven letter is eligible. For the second letter, there are only six possibilities because the letter used first will not be reused. Write the number of arrangements of the letters of the word KETCHUP using factorial notation.

Answer 1

Here,

" ! "Shows factorial

In ketchup there 7 different letters

7	6	5	4	3	2	1

Here, lets assume each block stands for the position of letter in the arrangement

Assuming there is no repitition of letters being allowed

1st position or block can be filled in 7 different ways

2nd block cam be filled out in 6 different (remaining) ways

3rd block can be filled out in 5 different ways

4th block .....4 different ways

5th block .. 3 different ways

6th block .. 2 different ways

7th block ..1 different way

That is

the total number of  different combinations possible = 7*6*5*4*3*2*1 = 7!

= factorial of 7 = 7*720

= 5040 different words