Question

In how many different ways can the letters of the word MONDAY be arranged ? How many arrangements begin with M ? How many begin with M and do not end with N ?

Answer 1

Solution :-

Given word MONDAY

Total ways to arrangement 6 letters = $6!$

we have to find arrangement so that,

(i)

words so formed begin with M

No. of choice for $1^{st}$ letter = 1

For $2^{th},3^{th},4^{th},5^{th}and{6}^{th}$ letter, number of choices = 5, 4, 3, 2, 1

$\therefore$ Number of ways = $1\times 5\times 4\times 3\times 2\times 1=120$

(ii)

words so formed begin with M and don't end with N

Total letters = 6

No. of choice for $1^{st}$ letter = 1

No. of choice for last letter = 4

For $2^{th},3^{th},4^{th},5^{th}$ letters no. of choice = 4,3,2,1

$\therefore$ Number of ways = $1\times 4\times 4\times 3\times 2\times 1=96$