73.4k views
3 votes
A committee of eight congressman will be selected from a group of 11 Democrats and seven Republicans. Find the number of ways of obtaining a committee with exactly 3 Democrats.

User Gulnaz
by
7.4k points

2 Answers

4 votes

Answer:


3465

Explanation:

GIVEN: A committee of eight congressman will be selected from a group of
11 Democrats and
7 Republicans.

TO FIND: The number of ways of obtaining a committee with exactly
3Democrats.

SOLUTION:

Total number of congressman in committee
=8

Total number of republicans available
=7

Total number of democrats available
=11

As, the committee should have exactly
3 democrats, there will be
5 republicans in committee

No. of ways of selecting
3 democrats out of
11 democrats
^1^1C_3=(11!)/((11-3)!3!)


=(11!)/(8!3!)


=165

NO. of ways of selecting
5 republicans out of
7 republicans
^7C_5=(7!)/((7-5)!5!)


=(7!)/(5!2!)


=21

The number of ways of obtaining a committee with exactly
3 Democrats.


=\text{total ways of selecting 3 democrats}*\text{total ways of selecting 5 republicans}


=165*21


=3465

Hence there are
3465 ways to form a committee in which there are exactly
3 democrats.

User Gokhan Kurt
by
7.2k points
5 votes

Answer: 3,465

Explanation:

Given, Number of Democrats= 11

Number of Republicans = 7

Total persons in the group =18

Number of congressman will be selected from the group = 8

Now , according to the combinations , the number of ways of obtaining a committee with exactly 3 Democrats.= (3 Democrats , 5 Republicans)


=^(11)C_3*^7C_5\\\\=(11!)/(3!8!)*(7!)/(5!2!)\\\\=(11*10*9*8!)/(6*8!)*(7*6*5!)/(5!*2)\\\\=165*21=3465

Hence, the number of ways of obtaining a committee with exactly 3 Democrats. = 3,465

User Chroder
by
6.8k points