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8!

PARALLEL has 8 letters with one letter appearing 3 times and 1 letter appearing 2 times. The letters can be arranged in 8!/(3!* 2!) = **3360 ways**.

No. of Permutations=**3360**.

Hence, the number of words in which all do not come together = 3360-360 = **3000**. Q3.

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.

360 arrangements

∴ **360 arrangements** can be made using the letters of the word SCHOOL.
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So the total number of words using the letters of MUMBAI such that all the M’s come together are **120**. So this is the required answer.

There are **15,120 ways**.

You can form the required word in **576 ways**. Explanation: There are 4 odd places (since computer is a eight lettered word) and there are 3 vowels (u, e, o). Therefore, the vowels can be arranged in ways. The remaining 5 consonant can be filled up in the remaining 5 places in 5!

So there are 10 ways to put the P and L back in such that there are exactly 5 letters between them, so 90,720*10=**907,200** total such arrangements.

A total number of arrangements of 7 letters (here all distinct) is 7! And the total number of arrangements of grouped letters (Here U, I, E, I) is . Hence, a total number of words formed during the arrangement of letters of word UNIVERSITY such that all vowels remain together is equals to **60480**.

When arranging 2 letters of the word JULY, you have 4 choices for the first letter and 3 choices for the second letter. Number of permutations = Choices for 1 st letter Choices for 2 nd letter = 4 3= 12 ANSWER There are **12 ways** you can arrange 2 of the letters in the word JULY.

To find : Rank of word LATE in dictionary. Hence, The rank of the word LATE in arranging the letters of LATE in a dictionary among its permutations is **14**.

**2880**. Hope it is helpfull!!

So, there are **18,14,400 ways** in which the word ‘EXAMINATION’ can be arranged by keeping the first letter as ‘M’.

The word MATHEMATICS consists of 2 M’s, 2 A’s, 2 T’s, 1 H, 1 E, 1 I, 1 C and 1 S. Therefore, a total of **4989600 words** can be formed using all the letters of the word MATHEMATICS. Therefore, a total of 453600 words which begin with C can be formed using all the letters of the word MATHEMATICS.

So there are **360 different arrangements** of the word school.

s,h,o,o,l b. **s,c,h,o,l d**.

Words that can be made with school

**35 words** can be made from the letters in the word school.

120 ways

How many combination you can create by rearranging the alphabets of the word Indians so that the vowels always come together? = **120 ways**. The vowels (EAI) can be arranged among themselves in 3!
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Answer is option b)**720**.

The word MUMBAI consists of **6 letters** taht include two Ms. When we consider both the Ms as a single entity, we are left with 5 entities that can be arranged in 5! ways.

Hence, the total number of ways are **180**.

But out of these 4 letters E comes 2 times.

= 7*6*5*4*3*2*1 = **5040 ways**.

×(2!) =**10080**.

There are **11 letters** (including vowels) in “probability”.

How many arrangement are there of the letters DISAPPOINT? **10** is the total number of letters where 2 times P, 2 times I occurs in DISAPPOINT. for any assignment or question with DETAILED EXPLANATIONS!

Notice that in each case the number of arrangements is given by: (Total number of objects)! (Total number of objects – number of objects to be arranged)! The number of arrangements of n different objects taking r at a time is: **— =n**(n-1)(n-2)…. (n-r+1) n!

⇒Words with MOTE _ _ = 2! After this, we get the word ‘MOTHER’. So, there are **308 words** before the word ‘MOTHER’. word will be ‘MOTHER’ which is the rank of the word in the dictionary.

The number of 5-letter words is (65)⋅5! =**720**.

∴ **180 different** words can be formed with the letters of the word INDIAN.

=3360. Let su assume LLL as 1 letter. Then, LLL + PARAE has 6 letters, out of which there are 2 A’s and the rest are all distinct. Number of their arrangements =**6**!

question_answer Answers(1)

In a word ALGEBRA have 2 A’s and 5 different letters are there. 1) Two A’s will take 1 unit and 5 letters will take 5 units then total number units = 6. These can be arranged in 6! = 6x5x4x3x2x1 = **720 ways**.

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