Vinay D. answered • 03/30/16

Tutor

4.8
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Software Engineer with over 8 years of experience in programming.

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.