Singapore GCE O-Level · Additional Mathematics

Binomial expansion, permutations and combinations

31 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 31 questions

Find the coefficient of $x^{2}$ in the expansion of $(1 + x)^{6}$ .
Find the coefficient of $x^{2}$ in the expansion of $(1 + x)^{7}$ .
Find the coefficient of $x^{2}$ in the expansion of $(1 + x)^{8}$ .
Find the coefficient of $x^{3}$ in the expansion of $(1 + x)^{5}$ .
Find the coefficient of $x^{4}$ in the expansion of $(1 + x)^{9}$ .
Find the coefficient of $x^{3}$ in the expansion of $(1 + x)^{10}$ .
Find the coefficient of $x^{2}$ in the expansion of $(1 + 2 x)^{5}$ .
Find the coefficient of $x^{2}$ in the expansion of $(1 + 3 x)^{4}$ .
Find the coefficient of $x^{3}$ in the expansion of $(1 + 2 x)^{6}$ .
Find the coefficient of $x^{3}$ in the expansion of $(1 + 3 x)^{5}$ .
Find the coefficient of $x^{3}$ in the expansion of $(1 + 2 x)^{4}$ .
Find the coefficient of $x^{2}$ in the expansion of $(1 + 4 x)^{3}$ .
In how many ways can 5 different books be arranged on a shelf if only 2 of them are chosen and the order matters?
In how many ways can 6 different books be arranged on a shelf if only 3 of them are chosen and the order matters?
In how many ways can 7 different books be arranged on a shelf if only 2 of them are chosen and the order matters?
In how many ways can 8 different books be arranged on a shelf if only 3 of them are chosen and the order matters?
A committee of 3 members is to be chosen from 7 candidates. In how many ways can it be done?
A committee of 2 members is to be chosen from 8 candidates. In how many ways can it be done?
A committee of 4 members is to be chosen from 9 candidates. In how many ways can it be done?
A committee of 3 members is to be chosen from 10 candidates. In how many ways can it be done?
5 people stand in a row. Two of them, Amy and Ben, must stand together. How many arrangements are there?
6 people stand in a row. Two of them, Amy and Ben, must stand together. How many arrangements are there?
7 people stand in a row. Two of them, Amy and Ben, must stand together. How many arrangements are there?
How many different 3-digit numbers can be formed from the digits 1, 2, 3, 4 if no digit is used more than once?
How many different 3-digit numbers can be formed from the digits 1, 2, 3, 4, 5 if no digit is used more than once?
How many different 4-digit numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if no digit is used more than once?
Find the coefficient of $x^{2}$ in the expansion of $(3 - 2 x)^{4}$ .
Find the term independent of $x$ in the expansion of $(x + \frac{1}{x})^{6}$ .
Find the coefficient of $x^{3}$ in the expansion of $(2 - x)^{5}$ .
In how many different ways can the letters of the word LEVEL be arranged?
A team of $4$ is to be chosen from $6$ boys and $5$ girls. In how many ways can the team be chosen if it must contain exactly $2$ boys and $2$ girls?

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Binomial expansion, permutations and combinations

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