Math Is Fun Forum

A fair dice is rolled . the probability that the first time one occur at even no. of trails

Can any one explain me using Tree Diagram.

Thanks

In how many ways can the letters of the word SPECIAL be permuted if the vowels are to appear in alphabetical order

6 boys and 6 girls are sitting in a row . Then the no. of ways  that boys and girls sits alternatively

my solution::

Using gap method::

here X  = denote boys and _ = denote girl

Then X _ X _  X _ X _  X _ X _

first we can arrange boys , which can be done in 6! ways

now arrange girls in 7 gaps ,

for that first we select 6 place out of 7 which can be  done in C (7,6) ways and now arrange these 6 girls

Which can we done in C(7,6) * 6! = 7!

So total no. of ways is = 6! * 7!

but answer is = 2*6! *6!

so where i have done mistake

Thanks

If the equation \;

Then

if the vertices P, Q, R of a triangle PQR are rational points

Then which of the following points is(are) always rational point(s)

options.

(a)centroid  (b)incentre (c)orthocentre (d)circumcentreplz explain answer