Cominatroics

Question

There are 12 copies of Mathematics, 7 copies of Engineering, 3 different books on Medicine and 2 different books on Economics. Find the number of ways in which one or more than one book can be selected?
A. 3421 B. 3111
C. 3327 D. 3201

Answer 1

Ways of selecting  one or more books= Total number of selections possible $-$ Selection where no book is selected.

Total number of ways of selecting books = ways for selecting maths * ways of selecting engineering * ways of selecting Medicine *ways of selecting Economics.

Ways of selecting Maths = Not picking any+picking 1 maths +picking 2 maths+.....picking 12 maths = 1+1+1+...1 (13 times) =13.

Similarly ways of selecting engineering = 8

Ways of selecting Medicine= 2³ 

Ways of selecting Economics = 2²

Ways in which no book is selected is only one way i.e not selecting any book.

Hence total number of ways = (13*8*2³*2²)-1 = 3327

Comments

how way of selecting maths is 13?and not 2¹²

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Since all the maths book are copies of the same book, they are identical. So selecting any number of books can be done in 1 way. And not selecting any book is other way. So total of 12+1 =13 ways

Answer 2

12 copies of math= We can choose it in 13 ways

7 copies of Engineering= We can choose it in 8 ways

3 diff books for medicine, 2 diff books for economics = We can choose it in 2⁵ ways

So, total no. of selection $13\times 8\times 2^{5} -1$=3328-1=3327