Question

How many subsets of the set (m,a,t,h,c,o,u,r,s,e) contain at least one vowel? I'll give medals:)

Answer 1

Pleease anyone take a look:)

Answer 2

Just make all possible arrangements with vowels.

Answer 3

the vowels are a e i o u. I think in sets order doesn't matter.

Answer 4

@ primeralph

I can't do that because there are so many possibilities. Groups of 1, 2,3,4,5,6,7,8,and 9 are all poss.

Answer 5

spread it out
into
9 cases

9 letters
8 letters
7 letters
6...
...
1

Answer 6

No, the order does not matter

Answer 7

oh okay

Answer 8

so 9 Letters case is complete
what about 8 Letter case

Answer 9

@dan815
The problem is that there are sooo many possibilities for each case

Answer 10

why?

Answer 11

what are the conditions for your subset?

Answer 12

@dan815
Groups of 1, 2,3,4,5,6,7,8,and 9 are all poss.

Answer 13

@timo86m
the order doesn't matter and groups of 1, 2,3,4,5,6,7,8,and 9 are all poss. There aren't really any other conditions

Answer 14

so m is a subset :P lol

Answer 15

8 letters = just 9C8
7 Letters = 9C7
6Letters = 9C6
5Lettrs = 9C5
4 letters= here we gotta think a little (consider the case none of the 4 vowels get picked)

Answer 16

@dan815
Could you explain that?

Answer 17

lets split 4 letters using probabilities

Answer 18

4/9 = vowel, 5/9 =consonant

Answer 19

@timo86m
yes, m is a subset

Answer 20

look up combination formulas if order doesn't matter

Answer 21

http://www.mathwords.com/c/combination_formula.htm

Answer 22

Like nCr?

Answer 23

oh umm How i arrived at the letters from 9 - 5 is that no matter what combination i pick a vowel will always exist there

Answer 24

nCr is your anser :D

Answer 25

answer*

Answer 26

wait no that shud be till 9-6 letters we must think from 5 letters

Answer 27

For cases ; lets work these out now
5Letter
4Letter
3Letter
2Letter

Answer 28

Do you think we should work them out?

Answer 29

by the way, I don't think nCr works because nCr looks at the ORDER of things, not SETS Like, combinations involve order

Answer 30

I'd say:
Number of subsets with at least a vowel = Total number of subsets - number of subsets without vowel = A - B.
The two quantities on the right hand side are easier to compute.

A )Total number of subsets of a set of N elements: \(2^{N}\).
B) THe subsets not containing a vowel are ALL the subsets of {m,t,h,c,r,s}. same forumla but other numbers.

Answer 31

Answer So far
9 Letter=1
8 Letter=9C8
7 Letter=9C7
6 Letter=9C6
5 Letter=
4 Letter=
3 Letter=
2 Letter=
1 Letter=4

Answer 32

How is 9 letter equal to 1?

Answer 33

the whole thing is 10 letters, not 9