Secondary Maths, Very Easy!!!!

1. Find the number of different 9-letter arrangements which can be made with the letters of the word EQUATIONS if

i.) there is no restriction,

Answer: 9!

ii.) no 2 vowels can be placed next to each other.

Solution: As the rule,it should be only one as follow :

()represent non-vowels and (v) represent vowels.

(v)()(v)()(v)()(v)()(v)

Therfore,the answer is 5! x 4!


2. A committee of 5 students is to be selected from a group of 6 boys and 8 girls. In how many ways can this be done if

i.) the committee must be made up of students of the same sex,

The answer is 6C5+8C5

ii.) there must be at least 2 girls in the committee.

Solution:There are 4 ways when there must be at least 2 girls in
the committee.They are (3,2), (2,3), (1,4), (5,0).

Answer is 6C3 x 8C2 + 6C2 x 8C3 + 6C1 x 8C4+ 5C0

iii)One of the 8 girls is the sister of one of the 6 boys. Calculate the number of ways in which the committee can be formed given that both the siblings are among those selected

Solution:As the siblings must be chosen,there are ways to match the problem is (3,0), (2,1), (1,2), (0,3)

Answer is

5C3 x 7C0 + 5C2 x 7C1 + 5C1 x 7C2+ 5C0 x 7C3