Find how many arrangements can be made with the letters of the word “MATHEMATICS” in which the vowels occur together? -Maths 9th

Find how many arrangements can be made with the letters of the word “MATHEMATICS” in which the vowels occur together? -Maths 9th
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1 Answer

Answer :

(i) There are 11 letters in the word 'MATHEMATICS' . Out of these letters M occurs twice, A occurs twice, T occurs twice and the rest are all different. Hence, the total number of arrangements of the given letters =11!(2!)×(2!)×(2!)=4989600.=11!(2!)×(2!)×(2!)=4989600. (ii) The given word contains 4 vowels AEAI as one letter, we have to arrange 8 letters MATHMTCS + AEAI, out of which M occurs twice, T occurs twice and the rest are all different. So, the number of all such arrangements =8!(2!)×(2!)=10080.=8!(2!)×(2!)=10080. Now, out of 4 vowels, A occurs twice and the rest are all distinct. So, the number of arrangements of these vowels =4!2!=12.=4!2!=12. Hence, the number of arrangement in which 4 vowels are together =(10080×12)=120960.
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Related questions

The letters of the word ‘SOCIETY’ are placed at random in a row. What is the probability that three vowels come together ? -Maths 9th

Description : The letters of the word ‘SOCIETY’ are placed at random in a row. What is the probability that three vowels come together ? -Maths 9th

Last Answer : There are 7 letters in the word SOCIETY. ∴ Total number of ways of arranging all the 7 letters = n(S) = 7!. When the case of three vowels being together is taken, then the three vowels are considered as one unit, so the ... = 5! 3! ∴ Required probability = \(rac{5! imes3!}{7!}\) = \(rac{1}{7}\)

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Last Answer : The number of words formed from 'DAUGHTER' such that all vowels are together is 4320.

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Last Answer : Given: The word ‘SUNDAY’ Total number of letters in the word ‘SUNDAY’ is 6. So, number of arrangements of 6 things, taken all at a time is 6P6 = 6! = 6 ... of words using letters of ‘SUNDAY’ starting with ‘N’ and ending with ‘Y’ is 24

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In how many different ways can the letters of the word MULTIPLE be arranged so that the vowels always come together?

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Last Answer : We consider all the three vowels (U, I, E) as one letter, so total number of letters = 6, and three vowels can be arranged in 3! Ways among themselves. However, the letter ‘L’ comes twice. :. Total number of ways = (6! × 3!)/2! = 720 × 3 = 2160 Answer is: b)

In how many different ways can the letters of the word "ZYMOGEN" be arranged in such a way that the vowels always come together? a) 1440 b) 1720 c) 2360 d) 2240

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Last Answer : Answer: A)  The arrangement is made in such a way that the vowels always come together. i.e., "ZYMGN(OE)". Considering vowels as one letter, 6 different letters can be arranged in 6! ways; i.e., 6! = 720 ... in 2! ways; i.e.,2! = 2 ways Therefore, required number of ways = 720 x 2 = 1440 ways.

In how many different ways can the letters of the word 'VINTAGE' be arranged such that the vowels always come together? A) 720 B) 1440 C) 632 D) 364 E) 546

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In how many different ways can the letters of the word 'SPORADIC' be arranged so that the vowels always come together? A) 120 2 B) 1720 C) 4320 D) 2160 E) 2400

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How many arrangements can be made out of the letters of the word 'BIGBOSS' ? A) 9240 B) 2772 C) 1260 D) 1820 E) 2800

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Description : Could you please upload video tutorials in Mathematics for our convinence -Maths 9th

Last Answer : This answer was deleted by our moderators...

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In how many ways can the letters of the word EDUCATION be rearranged such that the relative positions of the vowels and the consonants remain the same as in the word EDUCATION? a) 9!/4 b) 4!*5! c) 4!*5 d) 9!-4!

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Last Answer : b) 4!*5!

In how many different ways can the letters of the word 'DILUTE' be arranged such that the vowels may appear in the even places? a) 36 b) 720 c) 144 d) 24

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Description : A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30cm long, 25 cm wide and 25 cm high. -Maths 9th

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Description : which of the following singular nouns changes vowels when made plural? -General Knowledge

Last Answer : The following singular noun changes vowels when made plural: Mouse.

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