Combinations - Exercise set 1

This exercise set contains some solved exercises on combinations. The theory needed to solve these exercises is introduced in the lecture entitled Combinations.

Exercise 1.1

3 cards are drawn from a standard deck of 52 cards. How many different 3-card hands can possibly be drawn?

Solution

First of all, the order in which the 3 cards are drawn does not matter (the same cards drawn in different orders are regarded as the same 3-card hand). Furthermore, each card can be drawn only once. Therefore the number of different 3-card hands that can possibly be drawn is equal to the number of possible combinations without repetition of 3 objects from 52. If we denote it by $C_{52,3}$ , then: [eq1]

Exercise 1.2

John has got 1 dollar, with which he can buy green, red and yellow candies. Each candy costs 50 cents. John will spend all the money he has on candies. How many different combinations of green, red and yellow candies can he buy?

Solution

First of all, the order in which the 3 different colours are chosen does not matter. Furthermore, each colour can be chosen more than once. Therefore, the number of different combinations of coloured candies John can choose is equal to the number of possible combinations with repetition of 2 objects from 3. If we denote it by $C_{3,2}^{\prime }$ , then: [eq2]

Exercise 1.3

The board of directors of a corporation comprises 10 members. An executive board, formed by 4 directors, needs to be elected. How many possible ways are there to form the executive board?

Solution

First of all, the order in which the 4 directors are selected does not matter. Furthermore, each director can be elected to the executive board only once. Therefore, the number of different ways to form the executive board is equal to the number of possible combinations without repetition of 4 objects from 10. If we denote it by $C_{10,4}$ , then: [eq3]

by Marco Taboga

About | Contacts | Privacy and terms of use | Sitemap