item a)
[tex]\displaystyle \frac{6! \ .\ 3! }{4! \. \ 2!\ }}=\frac{6.5.4! \ .\ 3.2! \ }{4! \ . \ 2! } =90[/tex]
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[tex]\huge\boxed{\displaystyle \frac{6! \ .\ 3! }{4! \ . \ 2! } =90}} \checkmark[/tex]
item b)
[tex]\displaystyle \frac{6! \ .\ 3! }{4! }}=\frac{6.5.4! \ .\ 3.2.1 \ }{4! } =180[/tex]
[tex]\huge\boxed{\displaystyle \frac{6! \ .\ 3! }{4! } =180}\checkmark[/tex]
item c)
[tex]\displaystyle \frac{6! }{4! } = \frac{6.5.4! }{4 !} = 30[/tex]
[tex]\huge\boxed{\displaystyle \frac{6! }{4! } = 30}\checkmark[/tex]
item d)
[tex]\displaystyle \frac{7! }{5! } = \frac{7.6.5! }{5 !} = 42[/tex]
[tex]\huge\boxed{\displaystyle \frac{7! }{5! } = 42}\checkmark[/tex]
