Question

all of the letters of the word DESPAIR are arranged in a row. If the Letters were arranged randomly, calculate the probability that: the vowels are together

That the first letter is A, given that the vowels are together?

Answer 1

1)vowels in DESPAIR = e,a,i =3
let eai be one 1 letter..so DESPAIR has 5 letters
to arrange them,,we have 5! ways
but eai can also exchange places 3! times
so final ans is 5! * 3!

2) now if A is first letter and the vowels remain together always,,
same way,,we have 5! ways
and eai can exchange places 2! times as A is fixed
so final ans here is 5! * 2!

hope that could help..

Answer 2

sorry sorry,,correction in 2nd part..

Answer 3

the 5 set of letters in despair can exchange places 4! times as set of vowels is fixed..and multiplying that by 2!,,ans is 4! * 2!

Answer 4

the number of arrangements of the letter is 7!

Number of arrangements with vowels together is 5! x 3!

P(vowels together) (5!x3!)/7! = 1/7

Vowels together 1st letter A = 5! X 2!

P(A 1st letter) = (5!x2!)/7! = 1/21

Answer 5

and yes,,for probability,,divide each ans by 7! ..sorry i missed that earlier,,damit!

Answer 6

and maybe i have even misunderstood the second part..gosh,,whats happening!

Answer 7

ages since I did this stuff... always rusty with it... so get someone to check mine

Answer 8

@campbell_st it looks all good to me except in part two you should have \(4!\cdot2!\) since you're only permuting the 4 letters d, s, p, r. and assuming that all the vowels are first.

Answer 9

i agree but it depends on the wording....does it mean A is first letter of word or just first of the vowels

Answer 10

thanks... 2nd part should be

4! x 2!

P(A 1st then vowels) = 4!x2!/7!

1/105

Answer 11

a is the first letter of the word, but the vowels are all together, so that means all the vowels must be before the rest of the letters.

Answer 12

hmmmm

Answer 13

I always disliked these questions...

Answer 14

the answer to the second part of this is 2!4!/ 3! 5! so 1/15
except im confused.... I understand part a though D:

Answer 15

why is it 2! 4! ?

Answer 16

why isnt it 2! X 5! ?

Answer 17

assume the vowels come 1st A is fixed... then there are 2 ways of arranging the remaining 2 vowels.... next comes the 4 letters D,S,P,R, the can be arranged in 4! ways

Answer 18

hence 2! x 4!

Answer 19

ohh so you dont make it 5!, (5 letters) because 2! cannot be moved around anyway?