Problema Solution
There are 10 books but only 7 will fit on the shelf. How many different ways can you choose and arrange 7 of them on your shelf?
Answer provided by our tutors
Here we are dealing with permutations.
A permutation is an ordered arrangement. The number of ordered arrangements of r objects taken from n unlike objects is:
nPr = n! / (n – r)!
where by definition n! = 1*2*3*....*(n-1)*n
in our case we have n = 10 and r = 7
10P7 = 10!/(10 -7)! = 10!/3! = 2*3*4*5*6*7*8*9*10/(2*3) = 4*5*6*7*8*9*10 = 604,800
there are 604,800 ways to arrange 7 books out of 10 on the shelf.