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divalli_oct07

Problems on number of functions-

Let A and B be two sets containing 'r' and 'n' elements. Then no.of functions from A to B are as follows:

NATURE NO OF FUNCTIONS

1)functions n^r

2)one-one ⁿp_rr<_ n

0 r >n

3)many to one (functions) - (one-one)

4)onto n^r -ⁿc₁(n-1)^r + ⁿc₂(n-2)^r- ......... r>_ n

0 r<n

5)into (functions) - (onto)

6)bijective r! = n! r = n

0 r

n

7)monotonic 2(^{n + r-1}c_r) - r

8)increasing or decreasing ^{n + r - 1}c_r

9)strictly increasing or strictly decreasing ⁿc_r n>r

Problems on geometrical applications-

let 'n' distinct points are on a plane.

CONDITION NO OF ST.LINES FORMED NO.OF TRIANGLES

FORMED

1)when no points

are collinear ⁿc₂ ⁿc₃

2)m of the n points

are collinear(m>2).

no other three points

are collinear ⁿc₂ - ^mc₂+ 1 ⁿc₃ - ^mc₃

3)n points are on a

circle ⁿc₂ ⁿc₃

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