Short Question 9 & 10

Question 9 (2 marks):
$\begin{array}{l}\left(\text{a}\right)\text{ Given }{}^{6}C{}_n>1\text{, list out all the }\\ \text{possible values of }n\text{.}\\ \left(\text{b}\right)\text{ Given }{}^{y}C{}_m={}^{y}C{}_n\text{, express }y\text{ in}\\ \text{terms of }m\text{ and }n\text{.}\end{array}$

Solution:
(a)
n = 1, 2, 3, 4, 5

(b)
y = m + n

Question 10 (4 marks):
Danya has a home decorations shop. One day, Danya received 14 sets of cups from a supplier. Each set contained 6 pieces of cups of different colours.

(a) Danya chooses 3 sets of cups at random to be checked.
Find the number of different ways that Danya uses to choose those sets of cups.

(b) Danya takes a set of cups to display by arranging it in a row.
Find the number of different ways the cups can be arranged such that the blue cup is not displaced next to the red cup.

Solution:
(a)
Number of different ways 3 sets of cups at random to be checked
= ¹⁴C₃
 =364


(b)


Number of ways (Blue cup and red cup are next to each other)
= 5! × 2!
= 240

Number of different ways the cups can be arranged such that the blue cup is not displaced next to the red cup
= 6! – 240
= 720 – 240
= 480