3 objects how many combinations

But if repetition is allowed then there are infinitely many combinations of all sizes that can be formed. Therefore, I shall assume that repetition is not allowed. Starting with 1 2 3 we can form combinations of size 1 2 or 3. For n things choosing r combinations we can count using the formula. That is a total of 7 combinations. If we wish to count choosing 0 items -- the empty combination -- as a combination, then we must add 1 way of doing that.

How many combinations can you make with the numbers 1,2,3? Mar 28, See a solution process below:. Thus, the number of permutations is 8! With possible permutations, the trifecta is a difficult bet to win.

The third rule of counting deals with event multiples. An event multiple occurs when two or more independent events are grouped together. The third rule of counting helps us determine how many ways an event multiple can occur.

Rule 3. Suppose we have k independent events. Event 1 can be performed in n 1 ways; Event 2, in n 2 ways; and so on up to Event k which can be performed in n k ways.

The number of ways that these events can be performed together is equal to n 1 n 2. Example 1 How many sample points are in the sample space when a coin is flipped 4 times? Solution: Each coin flip can have one of two outcomes - heads or tails. Use Stat Trek's Event Counter to quickly count event multiples. The Event Counter is free and easy to use. It can found in the Stat Trek main menu under the Stat Tools tab.

If we now had to choose 3 balls instead, it would be 5 3 permutations. In general, if we have n balls and we want to choose r balls with repetitions we have n r different permutations. Combinations - selections when order is not important 3. Combinations without repetitions How many ways are there to choose 3 balls out of our 5 balls from before if we can't repeat ourselves and we don't care about the order?

We can start off by seeing that the problem is similar to counting permutations without repetitions. Let's take a specific combination, say the balls 1, 2 and 3.

How many times does the combination appear in our permutation list? That's because there are 3! So if we choose 3 balls out of 5 with no repetitions, we have 5! Combinations with repetitions How many ways are there to choose 8 balls out of the 5 balls if we can repeat ourselves? How many permutations are there for 6 numbers? How many two digit even numbers are possible? How many combinations of 6 numbers are there in 59? Previous Article How do you calculate combinations?

Back To Top.