From a group of 13 women and 12 men, a researcher wants to randomly select 8 women and 8 men for a study. In how many ways can

Question

2 years ago

14

the study group be selected?

1 answer:

Fantom [35] · Answer 1 · 2023-05-20T08:13:36+03:00

The total number of ways the study can be selected is: 637065

Given,

Total number of women in a group= 13

Total number of men in a group = 12

Number of women chosen = 8

Number of men chosen = 8

∴ the total number of ways the study group can be selected = 13C₈ and 12C₈.

This in the form of combination factor = nCr

∴ nCr = n!/(n₋r)! r!

13C₈ = 13!/(13 ₋ 8)! 8!

= 13!/5!.8!

= 1287

12C₈ = 12!/(12₋8)! 8!

= 12!/5! 8!

= 495

Now multiply both the combinations of men and women

= 1287 × 495

= 637065

Hence the total number of ways the study group is selected is 637065

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From a group of 13 women and ​12 men, a researcher wants to randomly select 8 women and 8 men for a study. In how many ways can