Question

If $ n(A) = 4,n(B) = 3 $ and $ n(A \times B \times C) = 24, $ then $ n(C) $ is equal to
 $
  1)288 \\
  2)1 \\
  3)12 \\
  4)17 \\
  5)2 \\
  $

Answer 1

Hint: Here we are given the number of elements for the two sets and the product of the elements for three sets and so will take the correlation between the given and unknown terms and simplify for the required resultant value.

Complete step-by-step answer:
Here we will use the formula for $ n(A \times B \times C) = n(A) \times n(B) \times n(C) $
Place the given values in the above expression –
 $ 24 = 4 \times 3 \times n(C) $
Make the required term as the subject and move other terms on the opposite side. When the term multiplicative on one side moves to the opposite side then it goes to the denominator.
 $ n(C) = \dfrac{{24}}{{4 \times 3}} $
Find the factors of the term on the numerator of the right hand side of the equation.
 $ n(C) = \dfrac{{2 \times 3 \times 4}}{{4 \times 3}} $
Common factors from the numerator and the denominator cancels each other and therefore remove and
 $ n(C) = 2 $
From the given multiple choices – the fifth option is the correct answer.
So, the correct answer is “Option 5”.

Note: Always remember the basic standard formula for the product of the number of elements in two or more sets. Be good in multiples and division and also finding the factors of the terms and remember when the term is in the form of the fraction then to gets equivalent value by removing common factors from the numerator and the denominator.