Introduction for number of possible combinations:
In combinatorial mathematics, a k-combination of a finite set S is a subset of k distinct elements of S. Specifying a subset does not arrange them in a particular order; by contrast, producing the k distinct elements in a specific order defines a sequence without repetition, also called k-permutation. As an example, a poker hand can be described as a 5-combination of cards from a 52-card deck: the 5 cards of the hand are all distinct, and the order of the cards in the hand does not matter.
Between, if you have problem on these topics Law of Tangents, please browse expert math related websites for more help on What are Functions.
Formula for Number of Possible Combinations:
Number of possible Combinations formula is commonly used in probability and statistics. Number of possible combination formula solving is the number of possible combinations of several items from a set of items. We can write in a number of ways similar to:
nCr , Where,
r => number of possibilities in the thing,
n => complete possibilities in the thing.
Also it can be understand as “n select r”.
The formula for the number of possible combinations are given as follow:
n! n(n-1) (n-2) (n-r+1)
nCr = --------- = ----------------------------
r!(n-r!) r!
Example Problems for Possible Number Combinations:
1) From the group of 15 employees how many combinations are formed as an union of 3 employees?
Solution:
Solving Here n= 15 employees,
r = 3 teams
n!
nCr = ---------
r!(n-r!)
15!
15C3 = --------------
3! (15 – 3!)
15!
= -----------
3! (12)!
15*14*13
= --------------
3*2*1
= 5 * 7 * 13
15C3 = 455 possible number of combinations
2) From a group of 8 students the teacher chooses 4 students to give a demonstration. How many combinations are possible?
Solution:
n = 8 students
r = 4 students
Formula:
n!
nCr = ---------
r!(n-r!)
8!
8C4 = -----------
4! (8-4)!
8!
= -----------
4! (4)!
8*7*6*5
= -------------
4*3*2*1
15C4 = 70 possible number of combinations
3) In how many techniques can 5 girls be chosen this leaves four more girls to be chosen from the remaining 17 girls.
Solution:
The number of ways of arranging four boys from seventeen is 17x 16x 15x 14x 13
The number of methods of arranging the four among themselves is 5x4x3x2x1.
Therefore the number of ways of choosing the five girls,
17 x 16 x 15 x 14 x 13
= --------------------------
5 x 4 x 3 x 2 x 1
= 6188 combinations.
In combinatorial mathematics, a k-combination of a finite set S is a subset of k distinct elements of S. Specifying a subset does not arrange them in a particular order; by contrast, producing the k distinct elements in a specific order defines a sequence without repetition, also called k-permutation. As an example, a poker hand can be described as a 5-combination of cards from a 52-card deck: the 5 cards of the hand are all distinct, and the order of the cards in the hand does not matter.
Between, if you have problem on these topics Law of Tangents, please browse expert math related websites for more help on What are Functions.
Formula for Number of Possible Combinations:
Number of possible Combinations formula is commonly used in probability and statistics. Number of possible combination formula solving is the number of possible combinations of several items from a set of items. We can write in a number of ways similar to:
nCr , Where,
r => number of possibilities in the thing,
n => complete possibilities in the thing.
Also it can be understand as “n select r”.
The formula for the number of possible combinations are given as follow:
n! n(n-1) (n-2) (n-r+1)
nCr = --------- = ----------------------------
r!(n-r!) r!
Example Problems for Possible Number Combinations:
1) From the group of 15 employees how many combinations are formed as an union of 3 employees?
Solution:
Solving Here n= 15 employees,
r = 3 teams
n!
nCr = ---------
r!(n-r!)
15!
15C3 = --------------
3! (15 – 3!)
15!
= -----------
3! (12)!
15*14*13
= --------------
3*2*1
= 5 * 7 * 13
15C3 = 455 possible number of combinations
2) From a group of 8 students the teacher chooses 4 students to give a demonstration. How many combinations are possible?
Solution:
n = 8 students
r = 4 students
Formula:
n!
nCr = ---------
r!(n-r!)
8!
8C4 = -----------
4! (8-4)!
8!
= -----------
4! (4)!
8*7*6*5
= -------------
4*3*2*1
15C4 = 70 possible number of combinations
3) In how many techniques can 5 girls be chosen this leaves four more girls to be chosen from the remaining 17 girls.
Solution:
The number of ways of arranging four boys from seventeen is 17x 16x 15x 14x 13
The number of methods of arranging the four among themselves is 5x4x3x2x1.
Therefore the number of ways of choosing the five girls,
17 x 16 x 15 x 14 x 13
= --------------------------
5 x 4 x 3 x 2 x 1
= 6188 combinations.
