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37 questions
Additional Mathematics/Paper 1/Permutations and combinations
CAIEO-Level4037-o · Paper 1

Permutations and combinations

37 questions· page 1 of 4

Q122026 May/Jun·P113MMedium-Easy

Find the value of nn such that n+3C6=12×n+2C5^{n+3}\mathrm{C}_{6} = 12 \times {}^{n+2}\mathrm{C}_{5}.

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Q132026 May/Jun·P124MMedium

Show that, for all values of n≥3n \geq 3, n+2C3−nC3=n2^{n+2}\mathrm{C}_{3} - {}^{n}\mathrm{C}_{3} = n^2.

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Q122025 May/Jun·P114MMedium

In this question n≥6n \geq 6.

Use an algebraic method to show that nC5−n−1C5^{n}\mathrm{C}_{5} - {}^{n-1}\mathrm{C}_{5} can be written as n−1C4^{n-1}\mathrm{C}_{4}.

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Q112025 Oct/Nov·P123MMedium

Solve the equation (n−4) n+1C5=n+2C7(n-4)\,{}^{n+1}\mathrm{C}_{5} = {}^{n+2}\mathrm{C}_{7}.

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Q42024 May/Jun·P123 partsEasy
(a)

Find the number of teams that can be formed.

(b)

Find the number of teams that can be formed without any teachers.

(c)

Find the number of teams that can be formed with the same number of doctors as teachers.

Q72023 May/Jun·P113 partsEasy
(a)(i)

Find the number of different teams that can be chosen.

(a)(ii)

Find the number of different teams that can be chosen if the group of 15 people contains a family of 4 people who must be kept together.

(b)

Given that (n+9)×nP10=(n2+243)×n−1P9(n + 9) \times {}^{n}\mathrm{P}_{10} = (n^2 + 243) \times {}^{n-1}\mathrm{P}_{9}, find the value of nn.

Q72023 May/Jun·P124 partsMedium
(a)

Find the number of ways in which 14 people can be put into 4 groups containing 2, 3, 4 and 5 people.

(b)(i)

there are no further restrictions

(b)(ii)

the 6-digit number is divisible by 10

(b)(iii)

the 6-digit number is greater than 500000 and even.

Q72023 Oct/Nov·P125 partsMedium-Easy
(a)(i)

Find how many 6-digit numbers can be formed.

(a)(ii)

Find how many of these 6-digit numbers are divisible by 5.

(b)(i)

Find the number of committees that can be chosen.

(b)(ii)

Find the number of committees that can be chosen if all the doctors have to be on the committee.

(b)(iii)

Find the number of committees that can be chosen if there has to be at least one dentist on the committee.

Q52023 Oct/Nov·P134 partsEasy
(a)(i)

Find the number of passwords that can be formed.

(a)(ii)

Find the number of passwords that can be formed if the password has to contain at least one symbol.

(a)(iii)

Find the number of passwords that can be formed if the password has to start with two letters and end with two symbols.

(b)

A team of 8 people is to be chosen from 5 doctors, 4 teachers and 6 police officers.

Find how many possible teams have the same number of doctors as teachers.

Q82022 May/Jun·P123 partsMedium
(a)

A team of 6 people is to be chosen from 10 people. Two of the people are sisters who must not be separated. Find the number of different teams that can be formed.

(b)(i)

there are no other restrictions,

(b)(ii)

the password starts with two letters and ends with two digits.