Fun principle of counting A student works at the book store

(Fun principle of counting) A student works at the book store where she must work at least 4 and at most 5 days a week, at least one of which must be weekend day(Saturday or Sunday).

How many different weekly work schedules can she have?

Solution

We have two Cases:

(i) if she can work 4 days

(ii) if she can work 5 days

Taking Case-(i)

she can work 4 days:

In these we have Two cases:

(a) Three Working Days and One Weekend Days

(b) Two Working Days and Two Weekend Days

Taking Case (a)

To choose Three working days out of 5 working days=\" ⁵C₃\"

To choose One weekend days out of 2 working days=\" ²C₁\"

(⁵C₃)* (²C₁)=10*2=20

Taking Case (b)

To choose Two working days out of 5 working days=\" ⁵C₂ \"

To choose Two weekend days out of 2 working days=\" ²C₂\"

(⁵C₂)* (²C₂)=10*1=10

Taking Case-(ii)

she can work 5 days:

In these we have Two cases:

(c) Four Working Days and One Weekend Days

(d) Three Working Days and Two Weekend Days

Taking Case (c)

To choose Four working days out of 5 working days=\" ⁵C₄\"

To choose One weekend days out of 2 working days=\" ²C₁\"

(⁵C₄)* (²C₁)=5*2=10

Taking Case (d)

To choose Three working days out of 5 working days=\" ⁵C₃\"

To choose Two weekend days out of 2 working days=\" ²C₂\"

(⁵C₃)* (²C₂)=10*1=10

Adding all four Cases Results:

==> Case(a) + Case(b) + Case(c) + Case(d)

==> (20+10+10+10)=50

SHE CAN HAVE \"50\" DIFFERENT WEEKLY WORK SCHEDULES