Question

Roberto wants to display his 18 sports cards in an album. Some pages hold 2 cards and others hold 3 cards. How many different ways can Roberto display his figures?

Answer 1

Answer: There are 65 different ways Roberto can display his figures.

Explanation:

Since we have given that

Number of sports cards in an album = 18

Number of cards some pages hold =2

Number of cards some other pages hold=3

Now, there are 4 cases to generate this shown as follow:

Case I:

If we consider 6 cards of 3 pages then it will make

`3* 6=18\ cards`

So, there is no cards of 2 pages .

So, different ways in this case will be

`^6C_6=1`

Case II:

If we consider 3 cards of 2 pages and 4 cards of 3 pages , then it will again becomes

`2* 3+4* 3=6+12=18`

So, different ways in this case is

`(7!)/(3!* 4!)=35`

Case III:

If we consider 6 cards of 2 pages and 2 cards of 3 pages then it will become

`6* 2+2* 3=12+6=18`

So, different ways in this case is

`(8!)/(6!* 2!)=28`

Case IV:

if we consider 9 cards of 2 pages then it will alone makes it

`2* 9=18`

there is no card of 3 pages,

So, different ways in this case is

`^9C_9=1`

So, total number of ways Robert can display his figures is

`1+35+28+1=65`

Hence, there are 65 ways to do so.