Respuesta :
Answer:
32760
Step-by-step explanation:
This is a permutation of 15 objects taken 4 at a time. To calculate this, we use the formula:
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]
In our case, n is 15 and r is 4:
[tex]_{15}P_4=\frac{15!}{(15-4)!}=\frac{15!}{11!}=32760[/tex]
The different ways of four team members from the group of fifteen be lined up for a photograph are [tex]\boxed{32760}.[/tex]
Further explanation:
The formula of permutation can be expressed as,
[tex]\boxed{^n{P_r}= \frac{{n!}}{{\left({n - r} \right)!}}}[/tex]
Here, “n” represents the total observations and “r” represents number of the observation has to be arranged.
Given:
Total number of members in group is 15.
Four members from a group of 15 are lined up for a photograph.
Calculation:
The total number of different ways of four team members from the group of fifteen be lined up for a photograph can be calculated as follows.
[tex]^n{P_r}=\dfrac{{n!}}{{\left({n - r} \right)!}}[/tex]
Substitute 15 for n and 4 for r in above equation
[tex]\begin{aligned}^{15}{P_4}&= \frac{{15!}}{{\left( {15 - 4}\right)!}}\\&=\frac{{15!}}{{11!}}\\ &=\frac{{15 \times 14 \times 13 \times 12 \times 11!}}{{11!}}\\&= 15 \times 14 \times 13 \times12\\&= 32760\\\end{aligned}[/tex]
Hence, the different ways of four team members from the group of fifteen be lined up for a photograph are [tex]\boxed{32760}.[/tex]
Learn more:
1. Learn more about inverse of the function https://brainly.com/question/1632445
2. Learn more about range and domain of the function https://brainly.com/question/3412497
3. Learn more about profit and loss https://brainly.com/question/2479097
Answer details:
Grade: High School
Subject: Mathematics
Chapter:Permutation and Combination
Keywords: different ways, select, combination, randomly picks, permutation, photograph, team members, group of fifteen, lined up, permutation.
