How many ways can the letter of the word MATHEMATICS be arranged so that the vowels are always together?
This section covers permutations and combinations. Show
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Arranging Objects The number of ways of arranging n unlike objects in a line is n! (pronounced ‘n factorial’). n! = n × (n – 1) × (n – 2) ×…× 3 × 2 × 1 Example How many different ways can the letters P, Q, R, S be arranged? The answer is 4! = 24. This is because there are four spaces to be filled: _, _, _, _ The first space can be filled by any one of the four letters. The second space can be filled by any of the remaining 3 letters. The third space can be filled by any of the 2 remaining letters and the final space must be filled by the one remaining letter. The total number of possible arrangements is therefore 4 × 3 × 2 × 1 = 4!
n! . Example In how many ways can the letters in the word: STATISTICS be arranged? There are 3 S’s, 2 I’s and 3 T’s in this word, therefore, the number of ways of arranging the letters are: 10!=50 400 Rings and Roundabouts
When clockwise and anti-clockwise arrangements are the same, the number of ways is ½ (n – 1)! Example Ten people go to a party. How many different ways can they be seated? Anti-clockwise and clockwise arrangements are the same. Therefore, the total number of ways is ½ (10-1)! = 181 440 Combinations The number of ways of selecting r objects from n unlike objects is: Example There are 10 balls in a bag numbered from 1 to 10. Three balls are selected at random. How many different ways are there of selecting the three balls? 10C3 =10!=10 × 9 × 8=
120 Permutations A permutation is an ordered arrangement.
nPr = n! . Example In the Match of the Day’s goal of the month competition, you had to pick the top 3 goals out of 10. Since the order is important, it is the permutation formula which we use. 10P3 =10! = 720 There are therefore 720 different ways of picking the top three goals. Probability The above facts can be used to help solve problems in probability. Example In the National Lottery, 6 numbers are chosen from 49. You win if the 6 balls you pick match the six balls selected by the machine. What is the probability of winning the National Lottery? The number of ways of choosing 6 numbers from 49 is 49C6 = 13 983 816 . Therefore the probability of winning the lottery is 1/13983816 = 0.000 000 071 5 (3sf), which is about a 1 in 14 million chance.
Post your comments here:Name *: Email : (optional) » Your comments will be displayed only after manual approval. How many ways can MATHEMATICS be arranged so that the vowels come together?Thus, we have MTHMTCS (AEAI). Number of ways of arranging these letters =8! / ((2!)( 2!)) = 10080. How many ways can the letters of the word MATHEMATICS be arranged so that the vowels come together Brainly?So total 120960 ways. How many ways can the letters in MATHEMATICS be arranged?There are 24 different ways to arrage the letters in the word math . How many arrangements can be made with the letters of the word MATHEMATICS if all vowels dont occur together?Mathematic can be arranged in 453,600 different ways if it is ten letters and only use each letter once. Assuming all vowels will be together 15,120 arrangements. How many ways can MATHEMATICS be arranged so that the vowels come together?Thus, we have MTHMTCS (AEAI). Number of ways of arranging these letters =8! / ((2!)( 2!)) = 10080.
How many arrangements can be made with the letters of the word MATHEMATICS if all vowels dont occur together?Mathematic can be arranged in 453,600 different ways if it is ten letters and only use each letter once. Assuming all vowels will be together 15,120 arrangements.
How many ways can the letters in MATHEMATICS be arranged?There are 24 different ways to arrage the letters in the word math .
How many ways to arrange the letters in MATHEMATICS if the vowels are always together at the end of Word?120960 ways . Originally Answered: In how many different ways can the letters of the word mathematics be arranged so that the vowels always come together?
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