How many permutations can be made using all the letters in the word DEFENSELESSNESS
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This section covers permutations and combinations. Show
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!
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. 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.
Submit 98.3% Successfully Done Question #220868 How many permutations can be made from all the letters in the word "MISSISSIPPI", under the condition that "M" is not in the middle? Expert's answer Number of permutation in the word "MISSISSIPPI": "N_1=\\frac{11!}{4!4!2!}=34650." Number of permutations if "M" is in the middle: "N_2=\\frac{10!}{4!4!2!}=3150." Number of permutations if "M" is not in the middle: "N=N_1-N_2=31500." Need a fast expert's response? Submit order and get a quick answer at the best price for any assignment or question with DETAILED EXPLANATIONS! CommentsNo comments. Be the first! Leave a commentRelated Questions
How many permutations can be made from letters of the word permutation?Total number of letters in the word permutation is 11 out of which there are 2 ts. So number of permutations= 11!/2!
How many different permutations can you make with the letters in the word 17?The letter N appears 2 time. The letter T appears 1 time. Hence, the total number of permutations with the letters in the word Seventeen. So, the correct answer is “7560”.
How many different permutations can be made with the letter of the word Tuesday so that the vowels are always together?=120×6×74×6×24=354. Was this answer helpful?
How many distinct permutations can be formed from all the letters of the word icicle?1 Answer. The Reqd. No. of Permutations=3360.
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