Question

An urn contains 17 red marbles and 18 blue marbles. 16 marbles are chosen. In how many ways can 6 red marbles be chosen?

Answer 1

Answer: N = 541,549,008

Therefore the number of ways to select 6 red marbles is 541,549,008

Explanation:

Given;

Number of red marbles total = 17

Number of blue marbles total = 18

Number of red marbles to be selected = 6

Number of blue marbles to be selected = 16 - 6 = 10

To determine the number of ways 6 red marbles can be selected N.

N = number of ways 6 red marbles can be selected from 17 red marbles × number of ways 10 blue marbles can be selected from 18 blue marbles

N = 17C6 × 18C10

N = 17!/(6! × (17-6)!) × 18!/(10! × (18-10)!)

N = 17!/(6! × 11!) × 18!/(10! × 8!)

N = 541,549,008

Therefore the number of ways to select 6 red marbles is 541,549,008

Answer 2

Total number of ways 6 red marbles can be chosen=541549008

Explanation:

16 marbles are chosen in which 6 are red marbles and remaining marbles ,which are 10, are blue marbles.

In order to find in how many ways 6 red marbles can be chosen we will proceed as:

Out of 17 red marbles 6 are chosen and out of 18 blue marbles 10 are chosen.

Total number of ways 6 red marbles can be chosen=
`17_(C_6) * 18_(C_1_0)`

Total number of ways 6 red marbles can be chosen=
`(17!)/(6!*(17-6)!) * (18!)/(10!*(18-10)!)`

Total number of ways 6 red marbles can be chosen= 12376*43758

Total number of ways 6 red marbles can be chosen=541549008