say you have 3 (different) books
about mathematics, 4 (different)
books about physics and 5 (different)
books about chemistry. in how many
ways can you arrange them in a shelf
such that no two books from the same
subject are adjacent?
the family A has 5 members and the
family B has 4 members. there are
6 personsfrom other families.
in how many ways can you arrange
these 15 persons around a round table
such that no member from family A
and no member from family B are
next to each other?
sequence of string said to be orderly
if element index i different to i+1
for example
aba has orderly value 2
abab has orderly value 3
abaabb has orderly value 3
if there are 7 a and 13 b
example
aaaaaaabbbbbbbbbbbbb has orderly value 1
what is the mean of its orderly value
for all possible sequences?
Prove that ∀n∈IN^∗
Σ_(k=1) ^(2^n −1) (1/(sin^2 (((kπ)/2^(n+1) ))))= ((2^(2n+1) −2)/3)
Give in terms of n Σ_(k=1) ^(2^n −1) (1/(sin^4 (((kπ)/2^(n+1) ))))
let S={a,b,c,d,e,f}
if we take any subset S (same subset is allowed),
it also can be S, which will form S if we join them,
order of operation does not matter
({a,b,c,d},{d,e,f}) is the same as
({d,e,f},{a,b,c,d})
how many ways can we choose?
f : [1, 3] →R , f(x) = (1/x)
A(1, 1)
B(1, (1/3))
B′(b, (1/b)) , b ≥ 1
Find
i. equation of line AB′
ii. equation of tangent T ′ to C_f at point
with x = ((1 + b)/2)
iii. Study relative positions of L_(AB ′) , T ′ to C_f