Question

Can you help me solve these:

6. From 10 mathematics students, four are chosen to represent a math symposium. In how many ways can this be done with no restrictions?

A) 210 B) 120 C) 200 D) 126 E) 160

7. From a group of 10 boys and 8 girls, 6 students are chosen at random. How many of these selections consist of exactly four girls?

A) 18564 B) 3150 C) 115 D) 225 E) 18500

8. From 14 mathematics students, seven are chosen to represent a math symposium. Kate said she will not attend if Bob is present. With this restriction, in how many ways can the choice of students be made?

A) 1968 B) 2100 C) 3432 D) 1848 E) 2640

9. A committee of SIX is to be chosen from four men and six women. Find the number of ways of choosing the committee if there are no restrictions.

A) 100 B) 200 C) 210 D) 150 E) 110

10. An art gallery has a total of 13 paintings by a particular artist; of these, six are oil paintings and seven are watercolor paintings. The art gallery is asked to provide a special exhibition of this artist's work but is restricted to showing only four of the paintings. Calculate the number of ways in which the four paintings can be selected for the exhibition if one particular painting must be included.

A) 220 B) 715 C) 210 D) 286 E) 495