How many ways can a person toss a coin 14 times so that the number of tails is between 11 and 13 inclusive

Step-by-step explanation:

Probability is the possibility for an event to occur or not to occur.

The formula for a combination is:

n choose r = n! / (r! x (n-r)!)

Given

n=14

r= 11 to 13

Hence, we shall add up the cases for 11 through 13.

nCr

14C11 + 14C12 + 14C13

14!/11!(14-11)! + 14!/12(14-12)! + 14!/13(14-13)!

= 14!/11!•3! + 14!/12!•2! + 14!/13!•1!

= 14*13*12*11!/11!•(3*2*1) + 14*13*12!/12!•(2*1) + 14*13!/13!•(1*1)

= 2184/6+182/2+14/1

= 364+91+14

= 469 ways

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl

idk

step-by-step explanation: