By using the definitions of combinations and permutations:
a) The first permutation is not defined.
b) N = (³C₂) / (⁴C₂) = 1/2.
<h3>How to evaluate the permutations and combinations?</h3>
A permutation:
ⁿPk is written as:
ⁿPk= n!/(n - k)!
(the denominator only appears if nk)
And a combination is written as:
ⁿCk = n!/(n - k)ka)
We have the product of two permutations, but there is a problem:3P4 The first number is the size of the set, and the second is the number of elements we take from that set.
In that permutation we have a set of 3 elements and we need to select 4, so that permutation is not defined.
b) (³C₂) = 3!/(3 - 2)!*2! = (3*2*1)/(2*1) = 3
(⁴C₂) = 4!/(4 - 2)!*2! = (4*3*2*1)/[(2*1)*(2*1)]
= 3*2 = 6
Then the quotient can be written as:
(³C₂) (⁴C₂) = 3/6 = 1/2.
Note that A quotient is seen as the outcome of dividing two numbers by each other.
Learn more about permutations and combinations:
brainly.com/question/11732255
#SPJ1
