Answer:
(a) How many are there to select 2 pairs of gloves?
10 ways
(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)
130 ways
Explanation:
For the above questions we apply that combination formula
(a) How many are there to select 2 pairs of gloves?
There are 5 pairs of gloves according to the question above, hence:
5C2 = 5!/2! × (5 - 2)!
= 5!/2! × 3!
= 5 × 4 × 3 × 2 × 1/2 × 1 × 3 × 2 × 1
= 10 ways.
Therefore, there are 10 ways to select 2 pairs of gloves
(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)
i) A way to select 4 gloves out of 10 gloves =
10C4 = 10!/4! ×(10 - 4)!
= 10!/ 4! × 6!
= 210 ways
ii) In order for 2 of the 4 gloves selected to be a pair, note that we have 5 pairs of gloves hence:
5 × 2⁴
= 80 ways.
Therefore, the number of ways which we can select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.) = 210 ways - 80 ways
= 130 ways