Find the number of ways in which 21 balls can be distributed among 3 persons suc

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Question
Find the number of ways in which 21 balls can be distributed among 3 persons such that each person does not receive less than 5 balls.
Options
A. 28
B. 14
C. 21
D. 7

Correct Answer

28

Explanation

Let x, y, z be the number of balls received by the three persons, then

$x ? 5, y ? 5, z ? 5 a n d x + y + z = 21$

Let $u ? 0, v ? 0, w ? 0 t h e n$

$?$ x + y + z =21

$?$ u + 5 + v + 5 + w + 5 = 21

$?$ u + v + w = 6

$?$ Total number of solutions = ${}^{6 + 3 - 1}C_{3 - 1} = {}^{8}C_{2} = 28$

More questions

2.
If 37 ¹/ ₂% of a number is 900,then 62 ¹/ ₂% of the number is?
Options
A. 1200
B. 1350
C. 1500
D. 540

3.
Subtracting 6% of A from A is equivalent to multiplying A by how much?
Options
A. 0.94
B. 9.4
C. 0.094
D. 94

4.
The price of rice has increased by 60%. In order to restore to the original price, the new price must be reduced by?
Options
A. 331/3%
B. 371/2%
C. 40%
D. 45%

6.
A student is required to secure at least 50% marks in order to pass an examination. He secured 50 marks which were less than the minimum passing marks by 50. The maximum marks of the paper are?
Options
A. 200
B. 250
C. 275
D. 300

7.
A furniture seller sells two tables at ? 1500 each. He earned a profit of 20% on one table and suffered a loss of 20% on the another table. Net profit or loss in this deal is?
Options
A. 4% loss
B. 4% profit
C. 10% loss
D. 10% profit

9.
25% of what amount of money is equal to 12 ¹/ ₂ of ? 180?
Options
A. ? 120
B. ? 75
C. ? 80
D. ? 90

10.
The monthly income of a person is ? 5000. If his income is increased by 30% then what is his monthly income now?
Options
A. ? 7000
B. ? 5500
C. ? 4500
D. ? 6500

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