7. A student club has twenty members: 6 seniors, 4 juniors, 5 sophomores, and 5 freshmen. (a) In how many different ways can the club select a president, vice-president, and secretary? (b) In how many different ways can a social committee with three members be selected? (c) In how many different ways can a committee of four people be selected if the committee must have a senior, a junior, a sophomore, and a freshman?
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7. A student club has twenty members: 6 seniors, 4 juniors, 5 sophomores, and 5 freshmen.
(a) In how many different ways can the club select a president, vice-president, and secretary?
(b) In how many different ways can a social committee with three members be selected?
(c) In how many different ways can a committee of four people be selected if the committee must have a senior, a
junior, a sophomore, and a freshman?
(d) In how many different ways can a group of three people be selected if the group must consist of members of the
same class (e.g. all juniors)?
(e) In how many different ways can a four-person committee be selected from the club members if it must contain
two seniors and two juniors?
(f) Consider the only the juniors and sophomores, and suppose that Alice and Bob are two of the juniors. How many
ways are there to divide up the nine students into two groups, one of which contains Alice and the other of which
contains Bob? (Note: A group may have as few as one student.)
Hi! Thank you for the question. As per the honor code, we are allowed to answer three sub-parts at a time so we are answering the first three as you have not mentioned which of these you are looking for. Please re-submit the question separately for the remaining sub-parts.
We have given,
A student club has twenty members
There are seniors,
juniors,
sophomores,
and freshmen.
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