Question

A student found 6 Mathematics books, 5 Physics books and 4 Chemistry books. If he buys at least one book of each subject, total number of ways is

• A. 29295
• B. 32768
• C. 4210
• D. 5120

Hint:

For “at least one”, first count all subsets using \(2^n\), then subtract the empty selection.

Answer 1

The Correct Option is A

Concept: If from n distinct objects we choose at least one object, number of ways is \[ 2^n-1 \] Selections from each subject are independent. Apply multiplication principle.

Step 1: Choose Mathematics books.
Total subsets \[ 2^6=64 \] Exclude choosing none. \[ 64-1=63 \]

Step 2: Choose Physics books.
\[ 2^5-1 \] \[ 32-1=31 \]

Step 3: Choose Chemistry books.
\[ 2^4-1 \] \[ 16-1=15 \]

Step 4: Apply multiplication principle.
\[ 63\times31\times15 \] \[ =1953\times15 \] \[ =29295 \] Hence \[ \boxed{29295} \]