The flag

The flag should consist of 3 different-colored stripes—available colors are white, red, blue, green, and yellow.
Specify:
A) number of all flags
B) number of flags with a blue stripe
C) number of flags with a blue stripe in the middle
D) the number of flags that do NOT have a red stripe in the middle

Correct answer:

a =  60
b =  36
c =  12
d =  48

Step-by-step explanation:

$$\begin{gathered} n=5 \\ a=n\cdot (n-1)\cdot (n-2)=5\cdot (5-1)\cdot (5-2)=60 \end{gathered}$$

$b=3\cdot 1\cdot (n-1)\cdot (n-2)=3\cdot 1\cdot (5-1)\cdot (5-2)=36$

$c=(n-1)\cdot 1\cdot (n-2)=(5-1)\cdot 1\cdot (5-2)=12$

$d=a-c=60-12=48$

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