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.

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

$3\times 6=18\ cards$

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

$2\times 3+4\times 3=6+12=18$

So, different ways in this case is

$\frac{7!}{3!\times 4!}=35$

Case III:

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

$6\times 2+2\times 3=12+6=18$

So, different ways in this case is

$\frac{8!}{6!\times 2!}=28$

Case IV:

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

$2\times 9=18$

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.

Answer 2

He can show his cards at least 9 different ways. I’m pretty sure it’s right.