JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Permutations and Combinations

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A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so that no bag is empty, is

(A)18
(B)36✓ Correct
(C)39
(D)72

Answer: (B)

Solution

With no bag empty, four distinct books in three distinct bags must follow the split

(2, 1, 1)

. Choose the two books that share a bag in

(2 4) = 6

ways, then distribute the three resulting groups among the three distinct bags in

3! = 6

ways:

6 \times 6 = 36.

Equivalently, the number of onto maps from four books to three bags is

3! S (4, 3) = 6 \cdot 6 = 36.

JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Single correct option

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