The value of 6! is 720.
The number of ways the two people can be chosen from the group of six is 30 ways.
The number of ways the group can be chosen is 20 ways.
The number of ways the six people can be placed in a line for a photo is calculated as;
[tex]= 6!\\\\= 6 \times 5 \times 4 \times 3 \times 2 \times 1\\\\= 720 \ ways[/tex]
The number of ways the two people can be chosen from the group of six is calculated;
[tex]= 6P_2\\\\= \frac{6!}{(6-2)! } \\\\= \frac{6!}{4!} \\\\= \frac{6\times 5 \times 4!}{4!}\\\\= 6\times 5 \\\\= 30 \ ways[/tex]
The number of ways the group can be chosen is calculated as;
[tex]= 6C_3\\\\= \frac{6!}{(6-3)! \times 3!} \\\\= \frac{6!}{3! \times 3!} \\\\=20 \ ways[/tex]
Learn more about permutation and combination here: https://brainly.com/question/4658834
