A Textbook of Higher Mathematics: Volume I (Paperback)

Some parts of the book

25. Out of 3n given things 2n are alike and the rest are different. In how many different ways can a selection of 2n things be made from the given 3n things.
[Hints: All 2n alike things can be selected in one way. (2n-1) alike things and another thing can be selected in "C1 ways.
So, the required number of selection
=1 ("C1 "C2 "C3 ·
"Cn)=1 (2" - 1) = 2".]
26. How many students are to be selected from a group of 14 students so that number of selections is the greatest.
26.1. Find the greatest number of selection.
26.2. Also find the greatest number of selections when the group consists of 15 students.
27. Find the total number of selections of at least one red ball from 4 red balls and 3 green balls if 27.1. balls of the same colour are different, 27.2. the balls of the same colour are identical. [Hints (27.1) Total number of ways of selecting at least one red ball = "C1 *C2 *C3 *C1 = 241 15.
Total number of ways of selecting green balls from 3 different green balls (including the case of no green ball) Co (3C1 3C2 3C3)=1 (23-1) = 8.
So, the required number of selections = 15 x 8 = 120.