Question-4

There are 5 hats numbered 1 to 5. These 5 hats should be distributed to 6 people with each person getting a maximum of one hat. What are the total number of ways in which the hats can be distributed to 6 persons?

• 120
• 24
• 30
• 720

Hint

Use the concept of factorial.

Answer

• 120
• 24
• 30
• 720

Solution

Given there are 6 people and there are 5 distinct hats that needs to be distributed. Since the sixth person will not get any hat, it can be considered he/she gets a dummy hat. So, the number of ways 6 hats (5 distinct hats and one dummy hat) can be distributed to 6 people is \(6!=720\).