what is the probability that these are selected?

Question

The question says: 
A hospital reduced its emergency staff from 32 physicians to 28. The chief officer claimed that 4 physicians were randomly selected for job termination. however, the 4 physicians chosen are the 4 oldest among the original 32 staff. Find the probability that when 4 physicians are randomly selected from a group of 32, the 4 oldest are selected?

it says the answer is 1/35,960 but i have no idea how to get that answer.
We're learning about permutations and combinations but i cant fit these number into the formulas!!?

Nick · Accepted Answer

Prob = (ways of choosing 4 from 4 oldest)/(ways of choosing 4 from 32)

Prob = C(4,4)/C(32,4) = 1/ 35960 <----

--------------------------------
Normally I wouldn't give a detailed explanation for a combinatorics question but:

Imagine you line up the staff in descending age order from left to right then make a selection for job termination by writing "ss" under four of the staff:

01 02 03 04 | 05 ... 30 31 32
ss.......ss..ss..ss

For *any* selection the first "ss" may be placed in 32 positions, the second  in one of the remaining 31 positions and so on up to 4 "ss"s, giving:

32*31*30*29 = 32!/28!

But the 4 "ss"s are identical and so we divide by 4! to avoid counting different permutations of the same choice. Hence:

32!/28!4! = C(32,4) choices.

Out of those there is only C(4,4) = 1 way that the selection is {01, 02, 03, 04}. The ways of placing the 4 "ss"s in the first 4 positions (excluding permutations).

fcas80 · Answer

Without regard to order, there is only 1 way to pick the 4 oldest out of 32.  There are 32C4 = 35960 ways to choose any 4 out of 32.  Answer:  1/35960.

Trending News

what is the probability that these are selected?

2 Answers