Answer:
There are 35 possible group of 3 socks from a total of 7
Step-by-step explanation:
Given
Number of unique socks = 7
Number of possible selection = 3
Required
Number of ways she can make her selection.
The question can be categorised as combination; reason being that words like "take" as used in the question points to combination or selection.
To solve this, we make use of combination formula.
nCr = nPr/r!
Where n = 7 and r = 3
By substitution, we have
7C3 = 7P3÷3!
Taking it one at a time
7P3 = 7!÷(7-3)!
7P3 = 7! ÷ 4!
7P3 = 7 * 6 * 5 * 4! ÷ 4!
7P3 = 7 * 6 * 5
7P3 = 210
3! = 3 * 2 * 1
3! = 6.
So,
7C3 = 210 ÷ 6
7C3 = 35.
Hence, there are 35 possible group of 3 socks from a total of 7
