How many outcomes are possible

The number of permutations for r objects from n distinct objects is denoted by n P r. The number of possible outcomes or Permutations is reduced, if n objects have identical or indistinguishable objects. For example, 9 P 3 or 9 P 3 or 9P3 denotes the Permutation of 3 objects taken at a time from group of 9 objects. One of the popular applications of permutations is to find how many distinct ways to arrange n letters. To shuffle all the alphabets in a word, supply the total number of letters in a word as n for total number of elements and n as r for taking any n elements at a time.

Therefore the number of permutations is n!. There are 36 possible outcomes: 6 for each die. If the numbers and letters can be repeated then there are 45,, possible outcomes. If the letters and numbers can not be repeated there are 32,, possible outcomes. There are 12 possible outcomes. There are 25 or 32 possible outcomes can you get by tossing 5 coins.

If the numbers or symbols are all different then 10 outcomes. The are 52 possible outcomes if you pick a card from a deck of You just have to multiply 4 by 2 to get the answer. If a spinner has six possible outcomes, then there are 36 62 permutations of outcomes from spinning it twice. Possible outcomes of a single dice are 6 1,2,3,4,5,6 So if 5 such dices are rolled then the number of possible outcomes are 6 mulitiplied by 6 five times.

If a coin is tossed 15 times there are or possible outcomes. Four outcomes, three combinations. However, if the number cubes are indistinguishable, then these represent distinct outcomes. Log in. Math and Arithmetic. See Answer. To understand how we get this formula, first consider the case where we want to find how many ways we can order all n objects. The first choice allows us n options, the second choice allows us n — 1 options, the third choice allows us n — 2 options, and so on, all the way down to 1.

The total number of possible orderings is the product of all these numbers, which we can write as n!. But this just leads us to the formula for permutations given above, which is illustrated in the following practice problem.

Practice Problem : A group of five horses is racing at a track. How many different ways can the horses place in the top three? Solution : We can calculate the number of ways the horses can place in the top three by calculating the number of permutations. Let's also consider the problem from a more fundamental perspective. For first place, there are five different possible horses. For each of these possibilities, there are four remaining possibilities for second place-we then multiply five and four.

For third place, we have three remaining possibilities for each of the preceding results--calculate the product of five, four, and three, which is We don't care about the last two places.

Note how the formula for permutations is related to our fundamental approach to the problem:. Thus, the result is Some problems require us to calculate a number of possible outcomes without respect to ordering. Such a case is a lottery drawing where all that is required to win is to pick the correct numbers in any order. This problem requires us to make a change to the formulas above so as to disregard cases that have the same set of objects, but with a different ordering.

Consider the case where selection is made without replacement. The number of permutations, n P k , uses the formula given above. We can alter this formula to disregard ordering by eliminating each ordering of each set of objects. Since we are choosing k objects from a set of n objects, those k objects can be ordered in k!

So, if we simply divide n P k by k! This is called the number of combinations of n taken k at a time, which is sometimes written.

Practice Problem : There are five remaining cards from a standard deck. If event x in this case the chicken, the beef and the vegetables can occur in x ways. And event y in this case French fries or mashed potatoes can occur in y ways. Video lesson How many outcomes are possible when a die is rolled three times? Search Math Playground All courses.