Question

A spinner is separated into equal sections numbered 1 through 8. The spinner is spun, and two number cubes are rolled. How many possible outcomes contain all odd numbers? 12 20 36 288

Answer 1

Option C. 36

Answer 2

Answer with explanation:

It is given that , a Spinner is separated into equal sections numbered 1 through 8.

Total Possible Outcome={1,2,3,4,5,6,7,8}=8

⇒When a Number cube is Rolled once, total possible outcome ={1,2,3,4,5,6}=6

⇒When a Number cube is Rolled twice, total possible outcome =6²=36

Total possible outcome of these three compound event

= 36 × 8

=288

⇒Total possible outcomes which contain all odd numbers

= Getting odd number on all three boxes

=[ Getting number {1,3,5,7} on first box] ×[ Getting numbers from set {1,3,5,} on Second and third box]

=[ Four numbers in a box can be arranged in 4 ways] ×[Three numbers in a box can be arranged in 3 ways]×[Three numbers in a box can be arranged in 3 ways]

= 4 × 3×3

=36

You must be thinking why not ,36 +36+36=108,by changing the Arrangement also.But here if you change the Order of arrangement of numbers then also you will get the same result.So, you can use the concept of Combination also.

`=_(1)^(4)\textrm{C}*_(1)^(3)\textrm{C}*_(1)^(3)\textrm{C} \\\\=4 * 3 * 3\\\\=36`

Option C