تمارين لـ permutations and combinations
1.
There are 20 people who work in an office together. Four of these people are selected to go to the same conference together. How many such selections are possible?
2.
There are 20 people who work in an office together. Four of these people are selected to attend four different conferences. The first person selected will go to a conference in New York, the second will go to Chicago, the third to San Franciso, and the fourth to Miami. How many such selections are possible?
3.
XXXXXX numbers for a product are to be made using three letters (using any letter of the alphabet) followed by two single-digit numbers. For example, JGR29 is one such XXXXXX number. How many such XXXXXX numbers are possible if neither letters nor numbers can be repeated?
4.
A 7-card hand is chosen from a standard 52-card deck. How many of these will have four spades and three hearts?
5.
In a new group of 15 employees at a restaurant, 10 are to be assigned as servers, 3 are to be assigned as hosts, and 2 are to be assigned as cashiers. In how many ways can the assignment be made?
6.
In how many ways can a first prize, a second prize and four identical third prizes be awarded to a group of 15 people?
7.
There are 10 students from whom 4 are going to be chosen to represent their school at a conference. If Jack, Anna or Chris, but only one of them, must be chosen, in how many ways can the students be chosen to go to the conference?
