Question

3. There are 5 routes from station A to station B and 4 routes from station B to C. Answer the questions

a. How many different routes are possible from station A to station C?
b. In how many ways can a person travel from A to C and come back from C to A? c. In how many ways can a person travel from A to C and return back to A by using different routes? ​

Answer 1

>> Answer

_________

`\:`

• Number (A.)

A = 5routes

b = 4routes

C = 5 × 4 = 20routes

.

• Number (B.)

C = 20routes

Soo :

20 × 20 = 20^2 = 400

.

• Number (C.)

(5 - 1) × (4 - 1) × 20 = 4 × 3 × 20

= 12 × 20 = 240

Answer 2

a)

A to B 5 routes and B to C 4 routes

Total options:

• 5*4 = 20

b)

A to C, 20 ways as above calculation.

C to A, 20 ways as well.

Total options:

• 20 * 20 = 400

c)

A to C, 20 ways

Return to A with different ways:

• (5 - 1)(4 - 1) = 4*3 = 12

Total options:

• 20 * 12 = 240