Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

In how many ways $12$ flowers can be divided into $4$ children such that all contains $3$ flowers to each child.
Option: 1
$220$

Option: 2
$150$

Option: 3
$1540$

Option: 4
$15400$

Answers (1)

best_answer

The given information is:

Number of flowers $=12$

Number of children $=4$

Number of flowers to each child $=3$

Pick first $3$ flowers from $12$ flowers,

Total no. of ways of choosing is:

$\frac{12 !}{(12-3) ! 3 !}=\frac{12 !}{9 ! 3 !}=220$

Pick next $3$ flowers from $9$ flowers,

Total no. of ways of choosing is:

$\frac{9 !}{(9-3) ! 3 !}=\frac{9 !}{6 ! 3 !}=84$

Pick next $3$ flowers from $6$ flowers,

Total no. of ways of choosing is:

$\frac{6 !}{(6-3) ! 3 !}=\frac{6 !}{3 ! 3 !}=20$

Pick last $3$ flowers from remaining $3$ flowers and the number of ways this can be done is $1$ .

Since the four groups are similar, there is no differentiation between them. Therefore, we need to divide it with $4 !=24$ .

The total numbers of ways:

$\frac{220 \times 84 \times 20}{24}=15400$

Posted by

chirag

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

50 mL of 0.2 M ammonia solution is treated with 25 mL of 0.2 M HCl. If pK_b of ammonia solution is 4.75, the pH of the mixture will be :
Option: 1 3.75
Option: 2 4.75

Trending Articles/News

anam-khan

BTech aspirant from north-east or UT? Apply for CSAB NEUT counselling 2025 today

anam-khan

JoSAA round 2 cut-off 2025 out; BTech closing ranks for top engineering courses at IITs

anam-khan

Goa Engineering Admission 2025: 1,415 eligible for BE seats; merit list on June 27

Latest Question