In order to conduct an experiment, five students are randomly

Brock Byrd

Brock Byrd

Answered question

2022-07-15

In order to conduct an experiment, five students are randomly selected from a class of 20. How many different groups of five students are possible?

Answer & Explanation

Alisa Jacobs

Alisa Jacobs

Beginner2022-07-16Added 13 answers

Step 1
This can be done using the choose function.
The number of combinations are given by:
( n k ) = n ! k ! ( n - k ) !
where n is the total number of students and k is the number of students to be picked. So we have n = 20 and k = 5 :
( 20 5 ) = 20 ! 5 ! ( 20 - 5 ) ! = 20 ! 5 ! 15 !
Step 2
Evaluate directly with a calculator: 20 ! 5 ! 15 ! = 15504
we can simplify this before calculation by hand:
20 ! 5 ! 15 ! = 20 × 19 × ... × 2 × 1 5 × 4 × 3 × 2 × 1 × ( 15 × ... × 1 )
= ( 20 × ... × 16 ) ( 15 × ... × 1 ) ( 5 × ... × 1 ) ( 15 × ... × 1 ) = ( 20 × ... × 16 ) 15 × ... × 1 ( 5 × ... × 1 ) 15 × ... × 1
= ( 20 × 19 × 18 × 17 × 16 ) ( 5 × 4 × 3 × 2 × 1 )
Step 3
Simplify the numbers matched up by color:
= ( 4 × 19 × 9 × 17 × 4 ) ( 1 × 1 × 3 × 1 × 1 )
= 3 × 4 × 4 × 17 × 19
= 48 × 323 = 15504 .

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