3 letters are chosen at random from the letters P, A, N, S, O, L. What is the size of the sample space of this experiment?
12
10
20
30
35
To determine the size of the sample space in this experiment, we need to find out how many different combinations of 3 letters can be selected from the given 6 letters: P, A, N, S, O, L.
The formula to calculate the number of combinations is given by nCr = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items to be selected.
In this case, n = 6 (since there are 6 letters) and r = 3 (since we want to select 3 letters).
Using the formula, we can calculate the number of combinations:
nCr = 6! / (3! * (6-3)!)
= 6! / (3! * 3!)
= (6 * 5 * 4 * 3!) / (3! * 3 * 2 * 1)
= (6 * 5 * 4) / (3 * 2 * 1)
= 120 / 6
= 20
Therefore, the size of the sample space of this experiment is 20.