PLEASE HELP i am so desperate and tired and need a good grade, please help a sister out

Question

Consider the spades in a standard deck of cards. Let the ace have a value of 1, with 2 through 10 having their numerical values, and with Jack, Queen and King each having a value of 10. Three cards are drawn, with replacement, from these 13 spades. How many different unordered draws will give a value total of 22? 

Answer 1

It has been a long time since I tried permutations and combinations but let me give a shot

 

See, you have 13 cards available and you want to draw 3 cards but the sum should be 22. Now, lets first see how many unique options give 22 as sum

 

1. 10 10 2

2. 10 9 3

3. 10 8 4

4. 10 7 5

6. 10  6 6

 

There are 6 unique combinations. But the list is unordered which means any number can come anywhere between q to 3 draws. Therefore, use permutation formula here. You have 3 spots available and how many number can fill each spot.

 

1. 10 10 2 gives 3 different ways

That is 10 10 2, 10 2 10, 2 10 10

2. 10 9 3 gives 6 different ways

That is 10 9 3, 10 3 9, 3 10 9, 3 9 10, 9 3 10, 9 10 3 

Similarly

3. 10 8 4 gives 6 different ways

4. 10 7 5 gives 6 different ways

5. 10 6 6 gives 3 different ways

 

Ans should be 24.