JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Permutations and Combinations

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The number of sequences of ten terms, whose terms are either 0 or 1 or 2, that contain exactly five 1s and exactly three 2s, is equal to

(A)360
(B)45
(C)2520✓ Correct
(D)1820

Answer: (C)

Solution

A sequence of ten terms is built from the symbols

0, 1, 2

. With five

1

s and three

2

s fixed, the remaining

10 - 5 - 3 = 2

positions are forced to be

0

s. The number of distinct arrangements of ten symbols comprising five alike of one kind, three alike of a second and two alike of a third is the multinomial coefficient

\frac{10 !}{5 ! 3 ! 2 !} = \frac{3628800}{120 \cdot 6 \cdot 2} = \frac{3628800}{1440} = 2520.

The number of such sequences is

2520

JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Single correct option

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