A class of students consists of 8 boys and 12 girls. a. How many ways can a comm

Question

A class of students consists of 8 boys and 12 girls.
a. How many ways can a committee of 6 be selected?
b. How many ways can a committee of 6 be selected if an equal number of boys and
girls are selected?
c. How many ways can a committee of 6 be selected if no boys are to be selected?
d. How many ways can a committee of 6 be selected if at least 5 boys are to be
selected?
e. Suppose two of the students do not get along. How many ways can a committee
of 6 be selected so that the two of them aren’t both selected?
f. Suppose two of the students are glued together and cannot be separated. How
many ways can a committee of 6 be selected?
g. Suppose the class wants to elect a president, vice president, secretary and
treasurer. How many ways can the 4 officers be selected?

Explanation / Answer

Ways in which r things can be selected from n=nCr
a)6 can be selected from 8+12=20 students in 20C6 ways=38760

b)3 boys and 3 girls=8C3 * 12C3=12320

c)No boys=8C6=28

d)atleast 5 boys=12C5*8C1 + 12C6=6336+924=7260

e)2 boys will be excluded from total students=18C6=18564

f)2 students will be treated as 1=19C6=27132

g)4 students can be selected in 20C4 ways and can be given any post in 4! ways=20C4*4!=116280

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