# PRACTICE WORD PROBLEMS ON COMBINATIONS WITH SOLUTIONS

Practice Word Problems on Combinations with Solutions :

Here we are going to see some practice questions base d on the concept combination.

## Practice Word Problems on Combinations with Solutions

Problem 1 :

A committee of 7 peoples has to be formed from 8 men and 4 women. In how many ways can this be done when the committee consists of

(i) exactly 3 women?

(ii) at least 3 women?

(iii) at most 3 women?

Solution :

Number of men  =  8

Number of women  =  4

(i) exactly 3 women?

Number of ways  =  4C3   8C4

=  4 (70)

=  280

(ii) at least 3 women?

Number of ways  =  (4C3   8C4) +  (4C4   8C3)

=  4(70) + 1(56)

=  280 + 56

=  336

(iii) at most 3 women?

Number of ways

=  (4C0   8C7) +  (4C1   8C6) +  (4C2   8C5 +  (4C3   8C4)

=  8 + 4(28) + 6(56) + 4(70)

=   8 + 112 + 336 + 280

=  736

Problem 2 :

7 relatives of a man comprises 4 ladies and 3 gentlemen, his wife also has 7 relatives; 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man’s relative and 3 of the wife’ s relatives?

Solution :

(i) 3 ladies from husband’s side and 3 gentlemen from wife’s side.

No. of ways in this case

= 4C3  4C3 = 4  4 = 16

(ii) 3 gentlemen from husband’s side and 3 ladies from wife’s side.

No. of ways in this case = 3C3  3C3 = 1  1 = 1

(iii) 2 ladies and one gentleman from husband’s side and lady and 2 gentlemen from wife’s side.

No. of ways in this case

= (4C4  3C1 (3C1  4C2) = 6  3  3 ⋅ 6 = 324

(iv) One lady and 2 gentlemen from husband’s side and 2 ladies and one gentlemen from wife’s side.

No. of ways in this case

=  (4C1  3C2 (3C2  4C1) = 4  3  3  4 = 144

Hence the total no. of ways are

=  16 + 1 + 324 + 144 = 485 ways

After having gone through the stuff given above, we hope that the students would have understood, how to solve word problems on combinations.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6