Promo: Why does 0 factorial equals 1? Video Lecture | Sets and Functions - JEE

why does zero factorial equals one for
an integer and greater than or equal to
one the factorial is the product of all
integers from then down to one that is
for any natural number in n factorial
equals n times n minus 1 times n minus 2
and so on up to 1 the factorial value of
0 is defined as equal to 1 there is
reason for this definition it is not
arbitrary
when thinking about combinations we can
drive a formula for the number of ways
of choosing Kate things from a
collection of n things the formula to
count out such problems is a fraction
whose numerator is n factorial and the
denominator is K factorial times and
minus K factorial where K is less than
or equal to end
now let's consider the scenario where we
want to calculate the number of
handshakes that occur when everybody in
a group of three people shakes hands
here an equals three and since a
handshake requires two people K equals
two keeping the values of N and K in the
above formula the total number of
handshakes computes two three
suppose that the number of people in the
group is too
obviously there is only one handshake
but what happens if we put N equals two
and K equals two in the formula we get
one divided by zero factorial which can
be written as 1 divided by X where X is
the value of 0 factorial 1 divided by X
must equal 1 because there is only one
handshake
the only value of 0 factorial that makes
sense here is 0 factorial equals 1 and
so we define 0 factorial equals 1