Answer: 24 (Khan Academy), It should be 12 because unique relates to combinations (no repeats) and not permutations.May 8, 2020
Therefore, we can arrange the letters in the word ‘FACTOR’ in 720 ways. Thus, this is the required answer.
The answer is 60.
The answer is 4! = 24. The first space can be filled by any one of the four letters.
This is simply 5! =120 different ways.
= 120 ways. The vowels (OIA) can be arranged among themselves in 3! = 6 ways. Required number of ways = (120 x 6) = 720.
A permutation of a set of distinct objects is an arrangement of the objects in a specific order without repetition. Example 1. If there are three distinct books. A, B, and C, how many different.
|2.||How many different 5-letter arrangements are there of the letters in the word moose?||Explanation Permutation: 5P5/2! The o repeats twice. =(5•4•3•2•1)/(2•1) = 120/2 = 60|
|Choose: 120 60 30 20|
So, the total number of unique choices we could make to get to an arrangement of reindeer is 5⋅4⋅3⋅2⋅1=120.
This can be done `7! = 5040` ways.
Note: 8 items have a total of 40,320 different combinations.
In how many different ways can the letters of the word “STUDENT” be arranged? Total ways of arrangements is, STUDENT = 7! = 5040.
In more general terms, if we have n items total and want to pick k in a certain order, we get: n! / (n – k)! And this is the permutation formula: The number of ways k items can be ordered from n items: P(n,k) = n! / (n – k)!
b) How many of those arrangements have b as the first letter? Set b as the first letter, and permute the remaining 6. Therefore, there are 6! such arrangements.
The letters of the word CAMBRIDGE are arranged such that the first five letters of the alphabet are in alphabetical order. Find the number of different permutations. [ANS: 3024] Only permutation should be used.
The letter of the word ‘apple’ can be arranged in 60 ways.
In how many ways can 2 different history books, 5 different math books, and 4 different novels be arranged on a shelf if the books of each type must be together? There are 34560 ways the books can be arranged.
ways to arrange the books on the shelf in the desired pattern. That is 720 ways.
Total possible arrangement of letters a b c d is 24.
There are 1440 ways so that P and Q occupy continuous positions.
11 letters can be rearranged in 11! ways.
720What will be the number of ways to arrange 10 elements out of which 6 are repeated.
So for 6 items the equation is as follows 6*5*4*3*2= 720 possible combinations of 6 items.
We call these permutations. This is expressed 10P8 and is just 10 times 9: 90 choices. Or perhaps you meant the number of 8 digit numbers (repetitions permitted) using the digits 0-9. In that case, each digit has 10 choices and there are 8 of them, so the answer is 108 = 100 000 000.
= 40320 – 4320 = 36000.
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