c) The equation can be rewritten as:
[tex] \frac{7 * 6!}{6! * 5!} * \frac{13 * 12 * 11 * 10!}{10!} [/tex]
6! and 10! in the numerator and denominator cancel out. Leaving you with:
[tex] \frac{7}{5!} * 13 * 12 * 11[/tex]
Simplify:
[tex] \frac{12012}{120} [/tex] = 100.1
d) (2 + 4)! = 6!
6 * 5 * 4 * 3 * 2 * 1
30 * 12 * 2
360 * 2
720
e) Just like in part c, we can rewrite the numerator:
[tex] \frac{26 * 25* 24!}{24! * 2!} [/tex]
The 24! in the numerator and denominator cancel out. Leaving you with:
[tex] \frac{26*25}{2*1} = \frac{650}{2} = 325 [/tex]
f) Just like part c and e, we can rewrite the denominator:
[tex] \frac{15! * 8!}{16 * 15!} [/tex]
15! cancels in both top and bottom. Leaving you with:
[tex] \frac{8!}{16} = 2520 [/tex]
