How many ways can the letters of the word ORGANISM be arranged so the third letter is G? 7 8 5040 40,320
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ORGANISM
The 3rd letter here is G, and for our arrangement also, we need the 3rd letter as G, which is fixed
Now, we have remaining 7 positions in which we need to arrange the other letters
_ _ G _ _ _ _ _
for 1st position we have 7 ways to fill i.e. all the remaining letters
after filling 1st, to fill 2nd position, we have 6 ways to fill, i.e. the remaining letters after filling 3rd and 1st position
Similarly, we have 5 ways to fill 4th position, 4 ways to fill 5th,.... and so on.
So, total number of words we can make =
7 x 6 x 5 x 4 x 3 x 2 x 1
= 7! = 5040
So, we have total 5040 words we can make.
The 3rd letter here is G, and for our arrangement also, we need the 3rd letter as G, which is fixed
Now, we have remaining 7 positions in which we need to arrange the other letters
_ _ G _ _ _ _ _
for 1st position we have 7 ways to fill i.e. all the remaining letters
after filling 1st, to fill 2nd position, we have 6 ways to fill, i.e. the remaining letters after filling 3rd and 1st position
Similarly, we have 5 ways to fill 4th position, 4 ways to fill 5th,.... and so on.
So, total number of words we can make =
7 x 6 x 5 x 4 x 3 x 2 x 1
= 7! = 5040
So, we have total 5040 words we can make.
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