Permutations and Combinations Structured Questions | Cambridge IGCSE Additional Mathematics

Question 1 of 3 · 10 marks

Permutations and Combinations · 3 - Line Arrangements & Gap Method

3 parts

Additional Mathematics 0606 · Question 1Paper 2 · Calculator[10 marks]

A group of 8 students consisting of 5 boys ( $B_1, B_2, B_3, B_4, B_5$ ) and 3 girls ( $G_1, G_2, G_3$ ) line up in a single row for a photograph.

$\ce{B1}$ $\ce{B2}$ $\ce{B3}$ $\ce{B4}$ $\ce{B5}$

Gap 1 Gap 2 Gap 3 Gap 4 Gap 5 Gap 6

Gap Method: 5 Boys create 6 available gaps for girls (no 2 girls adjacent)

(a)

Find the number of different arrangements in which the 3 girls stand together in a block.

[3]

(b)

Find the number of different arrangements in which no two girls stand next to each other.

[4]

(c)

Find the number of different arrangements in which student $\ce{B1}$ and student $G_1$ do not stand next to each other.

[3]