Answer: 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
[tex]3\times 6=18\ cards[/tex]
So, there is no cards of 2 pages .
So, different ways in this case will be
[tex]^6C_6=1[/tex]
Case II:
If we consider 3 cards of 2 pages and 4 cards of 3 pages , then it will again becomes
[tex]2\times 3+4\times 3=6+12=18[/tex]
So, different ways in this case is
[tex]\frac{7!}{3!\times 4!}=35[/tex]
Case III:
If we consider 6 cards of 2 pages and 2 cards of 3 pages then it will become
[tex]6\times 2+2\times 3=12+6=18[/tex]
So, different ways in this case is
[tex]\frac{8!}{6!\times 2!}=28[/tex]
Case IV:
if we consider 9 cards of 2 pages then it will alone makes it
[tex]2\times 9=18[/tex]
there is no card of 3 pages,
So, different ways in this case is
[tex]^9C_9=1[/tex]
So, total number of ways Robert can display his figures is
[tex]1+35+28+1=65[/tex]
Hence, there are 65 ways to do so.
