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

Step 1: Use the non-empty-subset rule.
Picking at least one item from $n$ distinct items can be done in $2^n-1$ ways.
Step 2: Mathematics books.
$2^6-1=63$ ways from the $6$ Mathematics books.
Step 3: Physics books.
$2^5-1=31$ ways from the $5$ Physics books.
Step 4: Chemistry books.
$2^4-1=15$ ways from the $4$ Chemistry books.
Step 5: Multiply the independent choices.
Total $=63\times 31\times 15$.
Step 6: Compute.
$63\times 31=1953$ and $1953\times 15=29295$, option (1).
\[ \boxed{29295} \]