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?

There are 65 different ways Roberto can display his figures.

Step-by-step 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

So, there is no cards of 2 pages .

So, different ways in this case will be

Case II:

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

So, different ways in this case is

Case III:

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

So, different ways in this case is

Case IV:

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

there is no card of 3 pages,

So, different ways in this case is

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

Hence, there are 65 ways to do so.

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