Question

There are 20 marbles in a bag. Each marble has a different design or color. How many ways can you draw 8 marbles from the jar? Is it permutation or combination.

Answer 1

The number of ways of selecting a combination of 8 marbles from a bag containing 20 marbles is 125970

Explanation:

The number of selecting 8 marbles from a bag of 20 marbles

A combination gives the number of possible order or arrangement in a collection of k items selected from a set of n items

`C_(n,k) = \dbinom{n}{k}= (n!)/(k!\cdot \left ( n - k \right )!)`

In the question, k = 8, and n = 20

Substituting the values of n and k in the above equation gives;

`C_(20,8) = \dbinom{20}{8}= (20!)/(8!*\left ( 20 - 8 \right )!) = 125,970`

Therefore, the number of ways of selecting 8 marbles from a bag containing 20 marbles is given by the combination C₂₀, ₈ = 125970.