When you use the digits 3 and 4 to make a number, the number 34 and 43 are different hence the order of the digits 3 and 4 is important. Solution: There are 4 letters in the word love and making making 3 letter words is similar to arranging these 3 letters and order is important since LOV and VOL are different words because of the order of the same letters L, O and V. Hence it is a permutation problem. Example 8: We need to form a 5 a side team in a class of 12 students. How many different teams can be formed?
Solution: There is nothing that indicates that the order in which the team members are selected is imoportant and therefore it is a combination problem. How many 3 digit numbers can we make using the digits 2, 3, 4, 5, and 6 without repetitions? 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. The factorial function symbol:! 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. For this calculator, the order of the items chosen in the subset does not matter. Also referred to as r-combination or "n choose r" or the binomial coefficient. In some resources the notation uses k instead of r so you may see these referred to as k-combination or "n choose k.
You have won first place in a contest and are allowed to choose 2 prizes from a table that has 6 prizes numbered 1 through 6. How many different combinations of 2 prizes could you possibly choose?
In this example, we are taking a subset of 2 prizes r from a larger set of 6 prizes n. A teacher is going to choose 3 students from her class to compete in the spelling bee. She wants to figure out how many unique teams of 3 can be created from her class of In this example, we are taking a subset of 3 students r from a larger set of 25 students n.
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