Question

In how many different ways can the letters of the word 'SALOON' be arranged for
the following:
(i) If two Os must come together.
(ii) If the consonants and vowels must occupy alternate places.​

Answer 1

Let us look at the Answer:

Step-by-step explanation:

The word SALOON consists of two O's and 3 vowels and 3 consonants.

i) If two O's are to be together, we consider the two O's as one

    total number of ways = 5!/2! = 5×4×3×2×1/2 = 60 ways.

ii) If vowels and consonants occupy alternate places, It can be done in two ways.

CVCVCV or  VCVCVC :  2(3! ×3!/2)  = 24 ways

Answer 2

Answer:

(i) 120

(ii) 36

Step-by-step explanation:

(i)

O's must to be gathered

so take two O's one side and consider as one

OO is 2 therefore 2!

And it is same so not to repeat

so it is 2!/2!=1

Now there are 5 place

OO =1

2nd place has 5 options

3rd place has 4 options

4th place has 3 options

5th place has 2 options

p=1*5*4*3*2

p=120

therefore If two O's must come together is 120 ways

(ii)

there are two way to form alternate place

1) CVCVCV

2) VCVCVC

SO

V=3!

and it has OO common

so V=3!/2!

V=3

and

C=3!

then p=(3!*3!/2!)2

p=(6*3)2

p=18*2

p=36