Math problems how many combinations

In how many ways can you arrange 5 different books on a shelf? In how many ways can you select a committee of 3 students out of 10 students? How many triangles can you make using 6 non collinear points on a plane? A committee including 3 boys and 4 girls is to be formed from a group of 10 boys and 12 girls. How many different committee can be formed from the group?

In a certain country, the car number plate is formed by 4 digits from the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 followed by 3 letters from the alphabet.

How many number plates can be formed if neither the digits nor the letters are repeated? Combinations Calculator. Calculate the number of combinations of n elements taken r at the time. Permutations Calculator.

Calculate the number of permutations of n elements taken r at the time. Privacy Policy. Search website. Combinations are easy going. You can mix it up and it looks the same. In fact, I can only afford empty tin cans. Well, we have 3 choices for the first person, 2 for the second, and only 1 for the last.

Indeed I did. So, if we have 3 tin cans to give away, there are 3! If we want to figure out how many combinations we have, we just create all the permutations and divide by all the redundancies. Writing this out, we get our combination formula , or the number of ways to combine k items from a set of n:.

Combination: Picking a team of 3 people from a group of Combinations sound simpler than permutations, and they are. You have fewer combinations than permutations. But when we want to select just 3 we don't want to multiply after How do we do that?

There is a neat trick: we divide by 13! This is how lotteries work. The numbers are drawn one at a time, and if we have the lucky numbers no matter what order we win! Going back to our pool ball example, let's say we just want to know which 3 pool balls are chosen, not the order.

In fact there is an easy way to work out how many ways "1 2 3" could be placed in order, and we have already talked about it. The answer is:. Another example: 4 things can be placed in 4! So we adjust our permutations formula to reduce it by how many ways the objects could be in order because we aren't interested in their order any more :. Notice the formula 16! So choosing 3 balls out of 16, or choosing 13 balls out of 16, have the same number of combinations:.

Also, knowing that 16! We can also use Pascal's Triangle to find the values. Go down to row "n" the top row is 0 , and then along "r" places and the value there is our answer.

Here is an extract showing row Let us say there are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla. Now, I can't describe directly to you how to calculate this, but I can show you a special technique that lets you work it out.