In how many ways can the letters of the word INDIVIDUAL be arranged

Question

In how many ways can the letters of the word INDIVIDUAL be arranged

Answer 1

This is a permutation question. The answer is: 

10 letters in INDIVIDUAL.

3 I's,  1 N, 2D's, 1 V, 1U, 1A, 1L.  There are 6 different letters. 

equation: 10! / 6! = 5040. enter equation on google search or use calculator or pen and pencil )

To use pen and pencil: 10x 9x 8x7x6x5x4x3x2x1 divided by 6x5x4x3x2x1 = 10x9x8x7= 5040. 

 

answer: 5040.

Answer 2

Benny, let's say there are 10 boxes to put letters in in any order.  You'd be able to put any of the 10 letters in the first box.  For the second box, then, you'd have the remaining 9 to choose from.  The third box, 8, etc.

 

So, your answer is 10! ways, or 10x9x8x7x6x5x4x3x2x1.  Hopefully you have a ! button on your calculator!