Page 184 - DMTH202_BASIC_MATHEMATICS_II

Unit 13: Combinations

If you contain a factorial key, you can place it in as 3!, times 5!, divided by 1!, divided by 2!, Notes
divided by 4!, divided by 1! and then press enter or =.
If you don’t contain a factorial key, you can shorten it as exposed above and then enter it in. It
is most likely best to abridge it first, because in some cases the numbers can get pretty large, and
it would be awkward to multiply all those numbers one by one.

This indicates that there are 15 draws that would include 2 RED and 1 WHITE marbles.

Self Assessment

Fill in the blanks:
1. A .................................. of n objects taken r at a time is a selection of r objects from a total of
n objects (r  n), where order does not matter.
2. Combination signifies .................................. of things.

3. The n and the r signify the similar thing in both the permutation and combinations, but
the .................................. varies.
4. The number of combinations is indicated by .................................. .

5. The dissimilarity among combinations and permutations is in combinations you are
counting groups and in permutations you are counting different methods to assemble
items with respect to ..................................

13.2 Restricted – Combinations

(a) Number of combinations of ‘n’ dissimilar things taken ‘r’ at a time, when ‘p’ particular
things are forever included = C .
n-p
r-p
(b) Number of combination of ‘n’ dissimilar things, taken ‘r’ at a time, when ‘p’ particular
things are forever to be excluded = C
n-p
r
Example: In how many manners can a cricket-eleven be selected out of 15 players? if
(i) A particular player is always selected,

(ii) A particular is never selected.
Solution:

(i) A particular player is always selected, it signifies that 10 players are chosen out of the
remaining 14 players.

=. Required number of ways = C = C
14
14
10 4
= 14!/4!x19! = 1365
(ii) A particular players is never selected, it means that 11 players are chosen out of 14 players.
 Required number of ways = C
14
11
= 14!/11!x3! = 364

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