6. How many vectors
1
(
x
1
, ..., x
k
)
are there for which
x
i
∈{
1
,
2
, . . . , n
}
and
x
1
< x
2
<
···
< x
k
.
Consider both of the cases
k > n
and
k
≤
n
.
That the subsets of size k are in bijective correspondence with the vectors x1, ...xk, where x1 < x2 < ... < xk.
Hence, since there are
subsets of size k, there are
vectors of the above f
For a given k, 1 ≤ k ≤ n, how many vectors (x1, x2, . . . , xk) are there for which each xi is a positive integer such that 1 ≤ x1 < x2 < · · · < xk ≤ n?
For a given k, 1 ≤ k ≤ n, how many vectors (x1, x2, . . . , xk) are there for which each xi is a positive integer such that 1 ≤ x1 < x2 < · · · < xk ≤ n?
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How many 'X's will be output? while (i <=3){ k=1: while (k <- i) { cout << "x"; cout << endl; ++i;)