Permutations and combinations
Practice section 3 of 10
Questions 13–18 in this collection
Practice questions
Worked example · 1 of 6
Partition children into unlabelled groups
In how many ways can a party of 10 children be divided into
(i) one group of 2 and one group of 8,
(ii) two groups of 5,
(iii) three groups of sizes 2,4 and 4?
CJC · Lecture · Example 10
Solution
Self-practice · 2 of 6
Divide ten people into repeated group sizes
Find the number of ways in which 10 people may be divided into three groups of 1, two groups of 2 and one group of 3.
CJC · Lecture · Self-Practice 3
Solution
Worked example · 3 of 6
Select indistinguishable beads by colour cases
A box contains 7 beads which are indistinguishable except for their colour, of which 3 are red,2 are blue,1 is white and 1 is green. Given that the order in which they are selected does not matter, how many ways can 3 beads be selected?
CJC · Lecture · Example 11
Solution
Self-practice · 4 of 6
Select three letters of ELEVEN without ordering them
Given that the order in which the letters of the word ELEVEN are selected does not matter, how many ways can 3 letters be selected?
CJC · Lecture · Self-Practice 4
Solution
Worked example · 5 of 6
Keep the consonants of MINIMUM together
If the letters of the word MINIMUM are arranged in a line at random, in how many ways can this be done such that all the consonants are together?
CJC · Lecture · Example 12
Solution
Worked example · 6 of 6
Separate the three vowels of ORANGE
In how many ways can the letters of the word ORANGE be arranged such that all the 3 vowels are separated?
CJC · Lecture · Example 13