Aptitude - Permutation and Combination - Discussion

Thanks for explaining the solution.

The given word consists of 10 letters.

No letters are repeated
we have to form a four-letter word and letters should not be repeated so;
_ _ _ _
Consider 4th place we have now 10 letters and one place to fill, So 10C1 possibilities are there
Now consider 3rd place we have 9 letters(one already used)and one place to fill, so 9C1 possibilities are there.

Now consider 2nd place we have 8 letters and one place to fill, so 8C1 possibilities are there
similarly, for 1st place, 7C1 possibilities are there.

Now multiplying them =10C1x9C1x8C1x7C1=10x9x8x7=5040.

Formula for Permutation nPr= n!/(n-r!)
For 10P4= 10!/(10-4!).
=> 10!/6!.
=>10x9x8x7x6x5x4x3x2x1
--------------------------------------
6x5x4x3x2x1
=>6x5x4x3x2x1 in both numerator and denominator will get cancelled.

Hence 10x9x8x7=5040.

@Krishna Kumar.

Formula for Permutation nPr= n!/ (n-r!) *r!

Thanks to all for explaining.

After Selecting the letters in(10 * 9 * 8 * 7) ways those letters can be re-arrange in 4! ways.....

So, according to me answer should be 5040 * 4!

How here permutation is used when there is condition letters should not be repeated?

Please explain.

Here why we are using permutation concept and also how we are saying 4 letters s not repeating?

Could me explain me ?

What if we had a repetition of letters? Explain.

I HAVEA DOUDT : 1O C P MEANS 10X9X8X7/(1X2X3X4)