Answer
$a$. $8,568 $
$b$. $658,008$
Work Step by Step
$a$. Total respondents = $40$
The graph shows that $45\%$ of the respondents squeeze from the middle.
Thus, the number of respondents who prefer to squeeze from middle = $45\%(40) = (0.45)(40) = 18$
Hence, the number of possible combinations of $5$ persons out of $18$ is:
$_{18}C_5= \dfrac{18!}{5!(18-5)!}$
$_{18}C_5= \dfrac{6402373705728000}{120(6227020800)}$
$_{18}C_5= 8,568$
$b$. Number of combinations of $5$ persons out of $40$ is:
$_{40}C_5= \dfrac{40!}{5!(40-5)!}$
$_{40}C_5= \dfrac{40!}{5!(35)!}$
$_{40}C_5= \dfrac{40(39)(38)(37)(36)(35!)}{5!35!}\\
_{40}C_5= 658,008$
