Three 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? A

Question

MAVERICK [17]

3 years ago

5

Three 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? A

ssume that the order of the letters matters. That is, PAN is different from APN

Mathematics

2 answers:

AVprozaik [17] · Answer 1 · 2022-05-09T22:42:29+03:00

AVprozaik [17]3 years ago

3 0

You need to find the number of permutations of the 6 different letters, taken 3 at a time.
$6P3=\frac{6!}{(6-3)!}=\frac{6\times5\times4\times3\times2\times1}{3\times2\times1}=120$
Therefore the sample space is 120 possible outcomes.

Allisa [31] · Answer 2 · 2022-05-10T00:21:33+03:00

Allisa [31]3 years ago

3 0

If all the letters are different,
Using combinations:

<span>6C3 =6! /3!* (6-3)!
</span>Simplifying,
6C3 = 6x5x4 /1x2x3
= 120/6
= 20 ways
Hence,
The size of the sample space will be 20.