Question

There are 14 girls and 12 boys all with distinct heights, what are the total number of orders they can stand in such that the heights of all the girls decrease as we go from left to right ?

Answer 1

Answer:

${26\choose14}\times 12!$

Step-by-step explanation:

Total number of students = 26

Out of these 26 students 14 girls can be chosen in ${26\choose 14}$ ways

For girls only one arrangement is possible and the 12 boys can be arranged in 12! ways. Therefore, total possible arrangement of the boys and girls that the girls height decrease from left to right

$=12! \times {26\choose 14}$

$=12!{26\choose 14}$

Let me know if the answer is correct and helpful.

Answer 2

Answer:

12! * ²⁶C₁₄  = 26!/14! = ²⁶P₁₂

Step-by-step explanation:

There are 14 girls and 12 boys all with distinct heights

=> Total = 14 + 12 = 26

14 Girls can be arranged out of 26 position

in  ²⁶C₁₄   ways   (as their Sequence matters)

Now remaining 12 positions & 12 boys can be arranged

in ¹²P₁₂ = 12! ways  ( as their Sequence does not matter)

so total possible combination = 12! * ²⁶C₁₄

= 12! * 26! / (14! * 12!)

= 26!/14!

or u can do it this way

12 boys out of 26 positions can be arranged in

²⁶P₁₂  ways

and remaining 12 girls can be arranged in 1 way only as their order of standing is defined

Total ways = ²⁶P₁₂

12! * ²⁶C₁₄  = 26!/14! = ²⁶P₁₂