Respuesta :
Answer:
The answer is 57, i just took the quick check.
A. 72
B. 40,320
c. 57
Step-by-step explanation:
A person can select 4 people out of 6 people in 57 different ways.
The correct answer is option (A)
What is combination?
These are selections made by taking some or all of a number of objects, irrespective of their arrangements.
Formula to calculate the combination:
[tex]^{n}C_{r} =\frac{n!}{r!(n-r)!}[/tex]
where, n is the number of items to be selected from. r is the number of items to be selected.
Formula to calculate the factorial:
n! = n × (n-1) × (n-2) ×. . . × 1
For given example,
No of ways a person can select 0 people out of 6 people:
[tex]=^{6}C_{0} \\\\=\frac{6!}{0!(6-0)!}\\\\=1[/tex]
No of ways a person can select 1 person out of 6 people:
[tex]=^{6}C_{1} \\\\=\frac{6!}{1!(6-1)!}\\\\=6[/tex]
No of ways person can select 2 person out of 6 people:
[tex]=^{6}C_{2}\\\\ =\frac{6!}{2!(6-2)!}\\\\=15[/tex]
No of ways person can select 3 person out of 6 people:
[tex]=^{6}C_{3} \\\\=\frac{6!}{3!(6-3)!}\\\\=20[/tex]
No of ways person can select 4 person out of 6 people:
[tex]=^{6}C_{4} \\\\=\frac{6!}{4!(6-4)!}\\\\=15[/tex]
For total number of ways we add the values,
Total
= [tex]^{6}C_{0} + ^{6}C_{1}+ ^{2}C_{2}+^{6}C_{3}+^{6}C_{4}[/tex]
= 1 + 6 + 15 + 20 + 15
= 57
Hence, we can conclude that a person can select 4 people out of 6 people in 57 different ways.
The correct answer is option (A)
Learn more about combination here:
https://brainly.com/question/13387529
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