Question

A jeweler has 15 diamond pendants and will display 4 of them from left to right in a glass case. In how many ways can he select and display the 4 pendants?

a) 32760
b) 360360
c) 3520
d) 30030

Answer 1

A

Explanation:

Essentially, the definition of permutation is that the number of ways of selecting r things from a total of n things. THe formula is:

`nPr=(n!)/((n-r)!)`

Where n! means n * (n-1) * (n-2) * ....

Here the total number of things is 15 diamond pendants (n = 15) and we need to select 4 diamond pendants (r = 4). plugging these into the permutation formula gives us the answer.

`nPr=(n!)/((n-r)!)\\15P4=(15!)/((15-4)!)\\15P4=(15!)/(11!)\\15P4=(15*14*13*12*11!)/(11!)\\15P4=15*14*13*12=32,760`

correct answer is A