Question

How many code symbols can be formed using 5 out of 6 letters A, B, C, D, E, F so that the letters

1. cannot be repeated
2. can be repeated
3. cannot be repeated but must begin with E
4. cannot be repeated but end with CAB.

Answer 1

Given letters are A, B, C, D, E and F

a) cannot be repeated

• First box can be filled up in 6 ways.
• Second box can be filled up in 5 ways.
• Third box can be filled up in 4 ways.
• Fourth box can be filled up in 3 ways.
• Fifth box can be filled up in 2 ways.

∴ By fundamental principle of multiplication, total number of code symbols = 6 × 5 × 4 × 3 × 2 = 720.

b) can be repeated

Since the letters can be repeated, all the 5 boxes can be filled up in 6 × 6 × 6 × 6 × 6 ways = 7776.

c) cannot be repeated but must begin with E

E

• Since the letters cannot be repeated,
• Second box can be filled up in 5 ways.
• Third box can be filled up in 4 ways.
• Fourth box can be filled up in 3 ways.
• Fifth box can be filled up in 2 ways.

∴ Total number of code symbols = 5 × 4 × 3 × 2 = 120.

d) cannot be repeated but end with CAB.

C

A

B

• Since the letters cannot be repeated,
• I box can be filled up in 3 ways.
• II box can be filled up in 2 ways.

∴ Total number of code symbols = 3 × 2 = 6.