How many 5-digit numbers from the
digits {0, 1, ....., 9} have?
(i) Strictly increasing digits
(ii) Strictly increasing or decreasing
digits
(iii) Increasing digits
(iv) Increasing or decreasing digits
3 men and 4 women are to sit on a
table. Calculate the number of
possible sitting arrangements if
(a) they sit in a row such that the
men must not sit next to each
other.
(b) they sit in circular pattern and
the clockwise and anticlockwise
orders are considered the same.
Number of ways..n
differrnt things be distributed
in r identical boxes so as
1)empty box is allowed
2)empty box not allowed
Number of ways...n identical
things be distributed to r
identical boxes so as
1)empty box allowed
2)empty box not allowed
soit K un corps; pour toute permutation
σ de S_n , on note P(σ) sa matrice dans la base
canonique de K^n .
montrer que deux permutations σ_1 et σ_2 sont
conjugues dans S_n si et seulement si
P(σ_1 ) et P(σ_2 ) sont semblables.
hi !
We store 5 objects in three discernible drawers. Suppose that the different ways of carrying out these arrangements are equally probable, calculate the probability that one of the 3 drawers contains at least 3 objects.
In how many ways can you divide 20
students into 5 groups with 4 students
in each group such that any two
students don′t meet each other in
more than one group.