Math Question?

Question

Letter strings are formed by choosing four of the six letters in the word YEOUCH and arranging them in order. How many such letter strings end with the letters Y and E (in either order) ?

I know the answer is 24, but I hoped somebody could explain it, thanks.

Answer 1

You are really just looking at the permutations of a four letter string, consisting of OUCH

For something this simple, no need to use a formula

For the first letter, 4 possiblities, 3 for the second, 2 for the third and 1 for the fourth. So 4! (4 x 3 x 2 x 1)

Answer 2

First, lets consider the 4 remaining letters that we have.

O,U,C,H can be arranged how many different ways? "Four Factorial" (written mathematically as 4!) is the computation you need to do. 4! = 4*3*2*1 = 24. To explain this just a bit further, you have four letters to choose from for the first spot in the arrangement, then 3 to choose from for the next space, then 2 letters to choose from in the next, and finally one last letter for the last remaining spot. There are 24 ways to arrange the letters O,U,C, and H.

But your questions has a twist. It says that the last 2 letters in the 6 spaces will be Y and E in EITHER ORDER!! That means that you can either end with 'YE' or with 'EY'.

Now, considering that you have 24 possibilities with O,U,C, and H ... you can have each of those end with YE ... AND ... you could have each of those end with EY.

That means you have 48 possibilities -- not 24. You have to take into consideration the alternate ending with all 24 possibilities.

The answer is 48.

Answer 3

If the last two letters are Y and E, then the first four letters must be OUCH (in some order).
- There are four choices for the first letter
- Once #1 is chosen, there are three choices for the second letter
- Once #1 and #2 are chosen, there are two choices for the third letter
- Once #1, #2 and #3 are chosen, there is one choice for #4.

Hence, the number of possible orders for the first four letters is 4*3*2*1 = 24.

HOWEVER... each of these 24 configurations of OUCH can end in either EY or YE.
Hence, there are actually 48 ways to arrange those six letters so that they end in either EY or YE!

Answer 4

_ _ _ _

we have six Characters and only 4 characters can be used for the first 2 spaces and only 2 for the last 2 spaces

If we use one of the 4 digits in the first space we can only use one of the 3 digits left for the second space

4 3 _ _

since we could only use two digits for the last two spaces, we could use either of them in the third space and the other one in the last space

4 3 2 1

to get the total number of possibilities we just multiply all of them

4x3x2x1

24

Answer 5

ok.

since we have y n e at each end (notice we have another string by replacing them with each other). in the middle, we have 4 choices for one slot, and 3 (since we took a letter for the other slot) choices for the other slot. making: y4x3e AND e4x3y. add these and you get 24.

contact me.

Answer 6

6x4=24