SOLUTION: I need help in this Q plz 10) The letters of word ALGEBRA a- How many diffrent ways the letters can be arranged in a row ? b- In how many ways of these arrangments the two A's

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Question 58276: I need help in this Q plz
10) The letters of word ALGEBRA
a- How many diffrent ways the letters can be arranged in a row ?
b- In how many ways of these arrangments the two A's are together?
c- In how many ways of these arrangments the two A's are not together?
Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
I'll take a stab at it- I could be wrong, though
Suppose ALGEBRA didn't have 2 A's?
Suppose it was ALGEBRX instead
Then I could pick 7 different letters for the first letter
I'd have 6 different letters to choose from for the 2nd letter
I'd have 5 different letters to choose from for the 3rd letter
etc.
The number of combinations would be
7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040
but X and A are treated differently
A . . . . .X
X . . . . .A
and
.A . . . . .X
.X . . . . .A
All these paired A's and X's should be treated as a single A . . . . .A pair
so, divide 5040 by 2.
5040 / 2 = 2520 possible words from ALGEBRA
The double AA can be 1st , second, third, etc
AA . . . . .
. AA . . . .
. . AA . . .
. . . AA . .
. . . . AA .
. . . . . AA
That's 6 different ways AA can appear
The words without the AA is simply 2520 - 6 = 2514

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
The letters of word ALGEBRA
a- How many diffrent ways the letters can be arranged in a row ?
7!/2!=2520
b- In how many ways of these arrangments the two A's are together?
Harness the A's together then you have 6!=720 arrangements.
c- In how many ways of these arrangments the two A's are not together?
2520-720=1800
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Cheers,
Stan H.