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

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.

$=_{1}^{4}\textrm{C}\times_{1}^{3}\textrm{C}\times_{1}^{3}\textrm{C} \\\\=4 \times 3 \times 3\\\\=36$

Option C