Let A = \left\{1,2,3 ... 10 \right\} and B = \left\{1,2,3 ... 20 \right\} A function is chosen randomly from A to B,what is the probability that it is non decreasing?
106total no. of functions is 2010
now, for function to be non decreasing.... we have either the function is constant or increasing
No. of functions where the function is continuously decreasing is:
20!/10! as order is to remain same (i.e. decreasing)
So, prob of continously decreasing function is 20!/10!.2010
so, desired prob is 1-20!/10!.2010 i.e. 1-20P10/2010
1can u explain
"No. of functions where the function is continuously decreasing is:
20!/10! as order is to remain same (i.e. decreasing)"
106is the answer correct btw.??
oh i din see ur doubt it will take some time for me to think and explain... pls wait....anyway is the ans correct? theres no point in explaining the wrong answer as u(and I) will get even more confused
62Let the values of f(i) be denoted by ni
we know the
n1= n0+k1
n2= n1+k2
n3= n2+k3
n10= n9+k10 <=20
take summation,
n10= n0+k1+k2+k3+....k10 <=20
we kknow that n0>=1
so we can replace this with 1+k0
thus,
k0+k1+k2+k3+....k10 <=19
thi sis done in 29C10 ways
total no of ways is 2010
hence the answer :)
24Sorry sir but I cant understand the solution....can you xplain it again plzzzzzz in a diff manner......[1]
