3. n! This is known as the quot;Choosequot;
= nCr
Formula:
formula.
(n r)!r!
n is the number of objects to choose from.
r is the number of objects to be arranged.
Example: You have 49 numbers in the 6/49 lottery to
choose from and want to choose 6 numbers for your ticket.
you will then have..
49!
49!
49C6 = = 13 983 816
=
(49 6)!6! (43)!6!
ways to make your ticket.
5. Example: How many differnt necklaces of 12 beads can each be
made from 18 beads of different colours?
In this question, you are to choose 12 beads from 18 beads.
∴ 18C12
Step 2:
Step 1:
18! This side takes care
The (12 1)!
of the circular
quot;Choosequot; (1812)!12! 2
permutation idea,
Formula
18! 11! since the necklace
(6)!12! 2 is a circle and can
be flipped over.
18 564 19 958 400
(18 564)(19 958 400)