Counting exercises

Exercise 1

Each of the 50 students in a graduating class studies English or Spanish. We know that 40 students study English and 20 raise Spanish. Determine the number:

1- Students who study both languages.

2-Students who only study Spanish.

3-Students who study one language and only one.

RP: 10; 10 and 40.

Exercise 2.

The music teacher surveys 150 high school students.

--116 like variety music.

--52 like traditional music.

--40 like both kinds of music.

How many students have not given their opinion?

Exercise3

A sports club has 35 members. 18 members play football, 16 play basketball, and 10 play both sports.

Determine the number of practicing club members:

1- Only football.

2- Not practicing either of the two sports.

Exercise 4.

Fatima has 10 scarves, 8 boubous and 6 pairs of shoes.

To go to a village party, she wants to wear a scarf, a boubou, and a pair of shoes.

How many different ways can she dress?

Exercise 5.

1-How many numbers of 5 digits can be written?

2-Among these numbers, how many are even?

3-How many of these numbers end with 9?

4-How many of these numbers end with 45?

RP: 900,000; 45,000; 9000 and 900.

Exercise 6.

1-How many numbers can be written with 5 distinct digits?

2-Among these numbers, how many are even?

3-How many of these numbers end with 9?

4-How many of these numbers end with 45?

RP: 27216; 13776; 2688 and 294.

Exercise 7.

A class of 20 students (8H and 12F) wants to elect an office of 3 members: a leader, a secretary, and an advisor.

1-How many offices can we form?

2-How many offices can be formed if the leader is an H?

3-How many offices can be formed if the secretary is a Woman?

4-How many offices can we form if MR X and MD Y refuse to sit together?

RP: 6840; 2736; 4104; 6732..

Exercise 8.

A class of 20 students (8H and 12F) wants to form a group of 4 members:

1-How many groups can we form?

2-How many groups can we form if we need a group leader who is a man?

3-How many groups can we form if we need an accountant who is a Woman?

4-How many groups can we form if MR X and MD Y refuse to sit together?

Exercise 8.

A graduating class consists of 20 Girls and 10 Boys. To participate in the high school's budding genius competition, we want to form a team of 5 students.

1-How many teams can we form?

2-Determine the number of teams comprising:

a) exactly 3 boys.

b) no girl.

c) at least one girl.

d) no more than two girls.

Exercise 9.

An urn contains 6 red balls and 4 white balls.

1-Two balls are drawn simultaneously from the urn.

a) How many possible draws are there?

b) How many draws are there knowing that the drawn balls are of the same color?

c) How many draws, knowing that the drawn balls are of different colors?