Question

5 roles A, B, C, D and E respectively, needs to be sequenced through a machine.

a.) How many ways can a sequence be made without restrictions on order?

b.) If A should be processed before B, but C, D and E can be inserted before and after A is processed, how many possible sequences are possible?

c.) If A should be processed before B, but C, D and E can be inserted before and after A is processed, how many possible sequences are possible?

Answer 1

5 roles A, B, C, D and E needs to be sequenced through a machine.

a.) How many ways can a sequence be made without restrictions on order?

- If there is no restriction of order then 5 roles can be sequenced in 5! ways

= 120

b.) If A should be processed before B, but C, D and E can be inserted before and after A is processed, how many possible sequences are possible?

- A should be processed before B. Thus, sequence AB is fixed

Now, C, D and E can be inserted before and after A is processed.

Thus, it will be either before AB or after AB as B follows A

and C,D,E can be arranged in 3! ways

Thus, total ways

= 1* 2*3! (multiplying by 2 as C,D and E can occur before or after AB)

= 12

C) it is same as b