Aspinner 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 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.

Option C