permutations and combinations- mixed 1 - maths excel class

Permutations and Combinations- Mixed 1

MathsExcelClass 3rdYrMary1

1. Justin has 6 Russian dolls as shown below:

a. Justin arranges all 6 dolls in a line. How many different arrangements are possible?

b. In how many of these arrangements will the dolls all be arranged in order of ascending height?

c. If Justin arranges the dolls at random, what is the probability that they will be in order of ascending height?

d. In how many of these arrangements will the dolls all be arranged in order of descending height?

e. In how many of these arrangements will the dolls have at least 1 out of height order (ie, they are neither all ascending/descending)?

f. Justin arranges just 4 of the dolls in a line. How many arrangements are possible?

g. Justin chooses 3 of the dolls at random to give to his younger sister. In how many ways can he do this?

2. In how many ways can a committee of 3 women and 3 men be chosen from a group of 5 women and 6 men?



3. Heili has 5 novels on her reading list that she must read for school.

a. Heili has the choice to buy each novel in either hardcover or paperback form. In how many different ways could she purchase her books?

b. If Heili buys her books at random, what is the chance that they are all the same form (all paperback or all hardcover)?

c. In how many ways can Heili read her books if she picks the order at random?

d. Two of the books will be studied in term 1 and must be read first in any order. Heili can then read the remaining books at random. How many arrangements are possible?

4. In how many ways can the letters in the word PINEAPPLE be arranged?

5. In how many ways can the letters in the word ANTARCTICA be arranged?

6. In how many ways can 5 people be seated at a round table?

7. 9 students queue up at the canteen for lunch.

a. In how many different ways can the queue be formed?

b. Of the 9 students, one group of 3 arrive five minutes before the others and get to line up at the front. In how many different ways can the queue now be formed?



8. The following figure shows a pattern of dots. No set of 3 dots are collinear:

How many different triangles can be made using 3 of the dots as vertices?

9. In a boarding school dormitory, there is a line of 4 beds as shown:

a. The school rules state that each of the beds must have either a maroon, navy or dark green cover. How many different arrangements are possible for this line of beds?

b. Apart from the 3 choices of colour for the covers, there is a choice of 2 sheet colours and 4 pillowcase colours. How many different combinations of cover, sheet and pillowcase are possible for a single bed?

c. If every bed is given a cover, sheet and pillowcase at random, how many different arrangements are possible for this line of beds? Leave your answer unsimplified.

d. If no 2 beds are allowed to have the exact same set of cover, sheet and pillowcase, how many different arrangements are possible for this line of beds? Leave your answer unsimplified.

. . . . . . .



10. Ten students are competing in an 800m race. In how many different ways can 1st, 2nd and 3rd be placed?

11. Jan goes to the supermarket with the following shopping list, arranged by the section of the supermarket in which various items can be found:

Leave all expressions unsimplified.

a. If Jan collects the items in a random order (regardless of section), in how many ways can she do this?

b. Jan collects each item in one section before moving onto another. If she can go to each section in any order, in how many ways can she do this?

c. In the supermarket, the cleaning and bathroom sections are very close to each other. If Jan collects all the food items first before the cleaning and bathroom items, in how many ways can she do this? (She still collects all items in a single section before moving onto the next, and can go to either the cleaning or bathroom section first).

permutations and combinations- mixed 1 - maths excel class

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