Mathematics 9709 · AS & A Level · Permutations and combinations
Permutations and combinations — practice question
A Social Club has $15$ members, with $8$ men and $7$ women. Its committee is made up of $5$ members.
(a)[4]
Find how many different committees can be formed from the $15$ members if the committee must contain more men than women.
(b)[3]
How many different ways are there to split the 15 members of the club into a group of 3, a group of 5 and a group of 7?
(c)[3]
In how many different ways can these 7 members be arranged so that Abel and Betty stand next to each other and Freya and Gino do not stand next to each other?
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use combinations correctly to count the acceptable cases, for example $^8C_x \times ^7C_{5-x}$ for suitable $x$.” …