Skip to content
dronacharya.ai
← JEE Main 2022 · 28 Jun · Shift 2
MathematicsSingle correct+4 / -1Question 3 of 90

JEE Main 2022 · 28 Jun · Shift 2, Mathematics question 3

The number of ways to distribute 30 identical candies among four children C1C_1, C2C_2, C3C_3 and C4C_4 so that C2C_2 receives atleast 4 and atmost 7 candies, C3C_3 receives atleast 2 and atmost 6 candies, is equal to :

Choose one option
Answer and worked solution

Official answer: D

Fix C2=c2∈[4,7]C_2=c_2\in[4,7] and C3=c3∈[2,6]C_3=c_3\in[2,6]. C1+C4=30−c2−c3C_1+C_4=30-c_2-c_3 has 31−c2−c331-c_2-c_3 solutions.

Sum. 20⋅31−5(4+5+6+7)−4(2+3+4+5+6)=620−110−80=43020\cdot31-5(4+5+6+7)-4(2+3+4+5+6)=620-110-80=430.

(D)

Topics:Distribution and arrangements
← Previous questionNext question →