Question

How many arrangements of the word VIBGYOR
are possible such that 'O' is in the middle but 'I' is
not next to 'O'?​

Answer 1

Given:

Word = VIBGYOR

To Find :

Arrangements of the word VIBGYOR in a way such that 'O' is in the middle but 'I' is  not next to 'O

Solution

Total words in  VIBGYOR = 7

Position of O is = 4th

Thus,

At first position there are 6 options.

At second position there are 5 options.

At third position there are 3 options as I can to be next to O.

At fifth position I can not be there, thus there are 2 options.

At sixth position there are 2 options as I can be considered.

At seventh position there is only 1 option left.

Thus, the combinations will be -

6 × 5 × 3 × 1 × 2 × 2 × 1

= 360

Answer: There are 360 combinations possible.

Answer 2

Answer:

480

Step-by-step explanation:

___O___ total ways in which remaining letters can be arranged in this fashion are 6!

now let's keep I and O together

___OI__ or __IO___ now the ways in which we can have these two are (5! + 5!)

Now to find the ways in which O can be in the centre and I is not next to it is equal to

6!-(5!+5!) = 480

Thankyou.