Arrange The Numbers Is There Only One Possible Arrangement I Am Desperate.

In How many ways the letters of the word RAINBOW be arranged in which vowels are never together?

-A2A-RAINBOW consists of 7 distinct letters, in which there are 3 vowels and 4 consonants.We have to find the total number of arrangements such that the vowels are never together. It could only be possible if consonants and vowels are placed alternatively.Let us arrange the  4 consonants such that there is a slot of1 l letter between ever consecutive consonants._ C _ C _ C _ C _ There are 5 alternate slots appear in the representation but we have only 3 vowels to fit in those 5 slots.3 slots from 5 empty slots can be selected in [math]^5C_{3} \ = 10 [/math] ways3 vowels can be arranged in those 3 selected slots in [math]^3P_{3} \ = 3! \ = 6[/math] waysConsonants shown as C in the representation can be arranged among themselves in [math]^4P_{4} \ = 4! \ = 24[/math] waysTherefore, the total number arrangements of letters of the word RAINBOW such that vowels are never together = [math]\ ^5C_{3} \cdot \ ^3P_{3} \cdot \ ^4P_{4} \ = 10 *  3! * 4! \ = 1440[/math] waysI hope it helps!

Find the arrangement that can be made by taking 4 letters of the word MATHEMATICS?

"MATHEMATICS" As you can see there are some letters(like m,t and a) in this word which is getting repeated. So, while selecting the letters for arrangement we should consider all the cases. At first, i am gonna explain how to select letters for different cases and then later how to arrange them.We have 11 letters in "Mathematics"in which there are2 M's , 2 T's , 2 A's and other letters H,E,I,C,S are singleSelection of the 4 lettersfirst case: Two alike and other two alikeIn this case we are gonna select the two letters which are alike. We have three choices M,T,A. Out of these, we have to select two(Because we have to select four letters and selecting two alike letters means selecting four letters). So, it can be done in 3C2 ways second case: Two alike, two different1 alike letter(which will mean two letters) can be selected in 3C1 ways and other 2 different letters can be selected in 7C2 ways.(as there will be 7 different letters).So, 3C1*7C2 waysThird case: All are differentThis can be done in 8C4 ways as there are 8 different letters(M,T,A,H,E,I,C,S) Arrangement:For the first case, there will be two alike letters. So, arrangement of these letters can be done in 4!/2!*2! waysFor the second case, there will be 1 alike letter and two different letters which can be arranged in 4!/2! waysFor the third case, all letters are different so it can be arranged in 4! waysSo, the final answer will be(3C2*4!/2!*2!) + (3C1*7C2*4!/2!) + (8C4*4!) = 18+ 756 + 1680 ways= 2454 ways

I met a guy through arranged marriage set up. I have no way to reach out to him. Would it be okay to send him a friend request on fb?

Sending friend request is not any crime yet. After all it's a social networking site :p) But yeah to answer your question i would relate yours thing to mine one. We (me and my love) met through an arranged marriage setup only. At that time we were of 20 and our parents wanted us to just book(like railway ticket) both of us so that their burden will get reduce. We both are educated and don't wanted to get marry so we went to met each other but didn't responded well. After few months of this incidence i got a message on facebook written "...??" although i knew she was her but still i behaved like i don't know her and asked do i know you. Then she gave her introduction and we both talked for 2days and decided that we both wont get marry so we gonna deny to our parents. Days and months passed (4months and 28days) and then her birthday came i was in dilemma that should i wish her or not on FB, but after thinking whole day i did on 23:59 "Wish you many many happy returns of the day" she replied "thanks" instantly, then we didn't talk again for (1 month and 26 days). And then i got sudden text from her. Since that day 20th june 2015 we are chatting, we exchanged out thoughts, contact numbers,etc. Slowly slowly we both started love each other and our these late nights chats went to video chat. I proposed her and she accepted.After proposing we had many fights, there was the time also when we didn't talk for 10 continuous days. Today our relationship is complicated but yeah I LOVE HER and somewhere she also does (Somewhere because of personal reasons).We are not married yet because we are just 22 now, and we don't  even know that we will get married to each other or not but yeah by chatting with her i came to know about people, i learnt about so many things like don't judge a book by its cover, people may have many flaws, etc.etc. But yeah by sending friend request you will come to know about him/her and there are chances that you may fall in love with him/her like we did.Thanks

In how many ways mississippi can be arranged?

11 total letters, 4i’s, 4s’s, 2p’s, 1m.Set out 11 “slots” for each letter to go in, and then pick 4 for the i’s. From the remaining 7, choose 4 for the s’s. From the remaining 3, choose 2 for the p’s, and then finally the 1 remaining slot can take the 1m.Ie - [math]{11 \choose 4}{7 \choose 4}{3 \choose 2}{1 \choose 1}=\frac{11!}{7!4!}\frac{7!}{4!3!}\frac{3!}{2!1!}\frac{1!}{1!}[/math] which simplifies to [math]\frac{11!}{4!4!2!1!}=34650[/math].