Question

There are 3 red chips and 2 blue chips. If they form a certain color pattern when arranged in a row, for example RBRRB, how many color patterns are possible?A. 10B. 12C. 24D. 60E. 100

Answer 1

Option A - 10

Explanation:

Given : There are 3 red chips and 2 blue chips. If they form a certain color pattern when arranged in a row, for example RBRRB.

To find : How many color patterns are possible?

Solution :

Total number of chips = 5

So, 5 chips can be arranged in 5! ways.

There are 3 red chips and 2 blue chips.

So, choosing 3 red chips in 3! ways

and choosing 2 blue chips in 2! ways.

As changing the places of similar chip will not create new pattern.

The total pattern is given by,

`T=(5!)/(3!* 2!)`

`T=(5* 4* 3!)/(3!* 2)`

`T=10`

Therefore, color patterns are possible are 10.

Option A is correct.