Permutations Flashcards
How many words can you rearrange from TOOTH? (assume that you must use all of the letters)
(5!) / (2!2!) = 30 possible rearrangements
Note: the 2!2! are for the two T’s and the two O’s
How many words can you rearrange from TOOTH if the word must start with a T? (assume that you must use all of the letters)
(2x4x3x2x1) / (2!2!) = 12 possible rearrangements
Note: the 2!2! are for the two T’s and the two O’s
How many ways can you rearrange the word ORANGE? (assume that you must use all of the letters)
6! or 6x5x4x3x2x1 = 720
How many 3 digit numbers less than 400 can you make, if the number must end in 4 or 5?
3x10x2 = 60 (1,2 or 3 for first digit 10 options (0 to 9) for second digit, 4 or 5 for last digit)
How many possible 5 digit numbers can you make if the number must be even and start with 7 or 8?
2x10x10x10x5 = 10000
How many 4 letter passwords can you make if you cannot repeat any letters?
26x25x24x23 = 358800
How many 4 letter passwords can you make if you can repeat the letters?
26x26x26x26 = 456976
If you have 8 students and you are lining up 5 of them for a photo, how many different photos can you take?
8x7x6x5x4 or 8P5 = 6720
How many different three letter passwords can you have if the password either has all vowels or all consonants?
5x5x5 + 21x21x21 = 9386
How many four letter words can you make from the words THREADS?
7x6x5x4 or 7P4 = 840
If you are lining up cars on a lot, and 2 cars are red, 3 cars are blue and 4 cars are black, how many ways can you line up the cars? (hint: the car model is the same for all)
(9!)/ (2!3!4!) = 1260
If you are arranging the letters in CAT, what is the probability that the arrangement will start with a consonant?
probability = favourable outcomes/total outcomes
(2x2x1) / (3x2x1) = 4/6 = 66%
If you are arranging the letters in TREES, what is the probability that the arrangement will start with a E?
arrangements starting with a E = 2x4x3x2x1 / 2! = 24
total arrangements = 5! /2! = 60
24/60 = 0.4 or 40%
