How Many 4 Letter Words Can Be Formed By The Word Mississippi 2t54s

How many 4 letter words can be formed by the word MISSISSIPPI?

This problem is really interesting in a way that it makes you think a bit as you have a lot of repeated letters and it could well be difficult if not approached in a right manner. There are 4 kinds of letters: 1 M, 2 Ps, 4 Ss and 4 Is available to form a 4-letter word. But we must not get confounded with the count of each kind of letters rather we must only consider the 4 kinds of letters: M, P, S and I. We can break down the number of 4 letter words that can be formed into sub-categories: 1. Words having all distinct letters 2. Words with exactly one letter repeated twice 3. Words with exactly one letter repeated thrice 4. Words with all letters of same kind 5. Words with two distinct letters, each repeated twice. Let us deal with each cases separately. 1. There are exactly 4 different kinds of letters: M,I,S and P. So, the total number of words with all distinct letters = 4! = 24 2. There are three different kinds of letters that can be repeated and they are I, P and S. The letter that has to be repeated can be selected in 3 ways. The two distinct letters can be selected in 3C2 =33C2 =3ways Also, each combination can be arranged in 4!2! =124!2! =12ways So, the number of words with exactly one letter repeated twice = 12 ∗ 3 ∗ 3C2 =10812 ∗ 3 ∗ 3C2 =108 ways 3. There are two different kinds of letters that can be used three times and they are I and S. The letter to be repeated thrice can be selected in 2C12C1 ways The remaining one letter can be selected in 3C1 =33C1 =3 ways Also, each combination can be arranged in 4!3! =44!3! =4ways So, the number of words with exactly one letter repeated thrice = 4 ∗ 2C1 ∗ 3C1 =244 ∗ 2C1 ∗ 3C1 =24 4. The letter could be either I or S. So, there are only 2 words: IIII and SSSS, in this case. 5. Two doubly repeated letters can be selected from P , I and S in 3C2 =33C2 =3 ways Each combination can be rearranged in 4!2!∗2! =64!2!∗2! =6 ways So, the total number of words with doubly repeated letters of two kinds = 3*6 = 18

Therefore, the total number of 4 letter words = 24 + 108 + 24 + 2 + 18 = 176 I hope it helps! 10.5k Views · View Upvotes · Answer requested by 1 person Upvote20 Downvote Comments1+ Share

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Shashank Goswami, Philomath Written Oct 7

here are 4 kinds of letters: 1 M, 2 Ps, 4 Ss and 4 Is available to form a 4-letter word. But we must not get confounded with the count of each kind of letters rather we must only consider the 4 kinds of letters: M, P, S and I. We can break down the number of 4 letter words that can be formed into sub-categories: 1. Words having all distinct letters 2. Words with exactly one letter repeated twice 3. Words with exactly one letter repeated thrice 4. Words with all letters of same kind 5. Words with two distinct letters, each repeated twice. Let us deal with each cases separately. 1. There are exactly 4 different kinds of letters: M,I,S and P. So, the total number of words with all distinct letters = 4! = 24 2. There are three different kinds of letters that can be repeated and they are I, P and S. The letter that has to be repeated can be selected in 3 ways. The two distinct letters can be selected in 3C2 =3ways Also, each combination can be arranged in 4!2! =12ways So, the number of words with exactly one letter repeated twice = 12 ∗ 3 ∗ 3C2 =108 ways 3. There are two different kinds of letters that can be used three times and they are I and S.

The letter to be repeated thrice can be selected in 2C1 ways The remaining one letter can be selected in 3C1 =3 ways Also, each combination can be arranged in 4!3! =4ways So, the number of words with exactly one letter repeated thrice = 4 ∗ 2C1 ∗ 3C1 =24 4. The letter could be either I or S. So, there are only 2 words: IIII and SSSS, in this case. 5. Two doubly repeated letters can be selected from P , I and S in 3C2 =3 ways Each combination can be rearranged in 4!2!∗2! =6 ways So, the total number of words with doubly repeated letters of two kinds = 3*6 = 18 Therefore, the total number of 4 letter words = 24 + 108 + 24 + 2 + 18 = 176 1.7k Views · View Upvotes Upvote1 Downvote Comment Share

Prakhar Dubey, worked at Capgemini India Written Oct 15

We are given the word MISSISSIPPI Now we have to form a 4 letter words from the letters of the word MISSISSIPPI. Here as some letters are being repeated and hence we can not simply go for P(11,4). Here we have to do it in cases. Let us first count letters and their repetition:— M— 1 I— 4 S— 4 P— 2 Case I: When all the four letters are distinct:-

P(4,4)=4!=24P(4,4)=4!=24 Case II: When two letters are repeated:the repeated letter can be selected from I,S,P i.e. C(3,1) and the remaining two letters can be selected from 3 i.e. C(3,2)

(3!/(2!∗1!))∗(3!/(2!∗1!)∗(4!/2!)(3!/(2!∗1!))∗(3!/(2!∗1!)∗(4!/2!) (6∗6∗24)/(2∗2∗2)(6∗6∗24)/(2∗2∗2) 108108 Case III: When one is repeated twice and another one is repeated twice:-

C(3,2)∗4!/(2!∗2!)C(3,2)∗4!/(2!∗2!) (3!∗4!)/(2!2!2!)(3!∗4!)/(2!2!2!) 6∗24/(2∗2∗2)6∗24/(2∗2∗2) 1818 Case IV: When one is repeated thrice and other is once:-

C(2,1)∗C(3,1)∗4!/3!C(2,1)∗C(3,1)∗4!/3! 2∗3∗24/62∗3∗24/6 2424 Case V: When one is repeated 4 times:-

C(2,1)∗4!/4!C(2,1)∗4!/4! 2∗4!/(4!)2∗4!/(4!) 22 Total number of 4 letter words formed from the letters of the word MISSISSIPPI can be computed by summing up the result of all these 5 cases.

i.e.24+108+18+24+2i.e.24+108+18+24+2 176176 Therefore total of 176 words can be formed from the letters of the word MISSISSIPPI. 992 Views · View Upvotes Upvote3 Downvote Comment Share

Mandeep Singh, enjoy P &C Written Oct 6

You would need to give more information about the question. 1.) Repetition of the alphabets is allowed or not ? 2.) Can the same alphabet be used again or not ? Assuming repetition is allowed and same alphabet can be used again Number of words possible :> .. Total alphabets = 4 ( M S P I ) NUmber of words = 4 x 4 x 4 x4

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