Priya and Padmini solve a problem on “How to count without actually counting” given in the text book as follows:
Find the number of ways in which a selection of 5 books can be done out of 3 physics, 3 chemistry and 3 mathematics books of taking at least one book of each subject, books of same subject being different.
Priya’s Solutions:
One book of each subject can be taken in $^{3} C_{1}$ ways balance 2 books from remaining 6 books can be taken in $^{6} C_{2}$ ways hence total no.of ways using fundamental principle of counting . $=^{3} C_{1} .^{3} C_{1} .^{3} C_{1} .^{6} C_{2}$
Padmini’s Solutions:
Number of ways in which atleast one Physics book can be selected $= (2^{3} - 1)$ perpendicularly one chemistry in $= (2^{3} - 1)$ ways and one mathematics in $= (2^{3} - 1)$ ways.
Total ways $= (2^{3} - 1) (2^{3} - 1) (2^{3} - 1)$
Which one of the following options is correct?

Question

Infinity Learn · Accepted Answer

Both Priya and Padmini are wrong and their answers are higher than the actual answer.

Detailed Solution