Answer:
Option D is correct.
The relation {(-8, -6) (-5, 2) (-8, 1) (7, 3)} is not a function.
Step-by-step explanation:
Given the relation: {(-8, -6) (-5, 2) (-8, 1) (7, 3)}
Domain is the set of all possible inputs of a relation i.e { -8, -5 , -8 , 7}
Range is the set of output values of a function i.e, {-6, 2 , 1 , 3}
The mapping as shown below in the figure:
A function is a relation in which every element of the domain is matched to not more than one element of the range.
In other words, we can say that ,no value of x gets mapped to more than 1 value of y.
Since, from the mapping you can see that the domain value -8 paired with -6 and 1; as x is used more than once.
Therefore, this relation is not a function
Answer:
a) 182 possible ways.
b) 5148 possible ways.
c) 1378 possible ways.
d) 2899 possible ways.
Step-by-step explanation:
The order in which the cards are chosen is not important, which means that we use the combinations formula to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
In this question, we have that:
There are 52 total cards, of which:
13 are spades.
13 are diamonds.
13 are hearts.
13 are clubs.
(a)Two-pairs: Two pairs plus another card of a different value, for example:
2 pairs of 2 from sets os 13.
1 other card, from a set of 26(whichever two cards were not chosen above). So
So 182 possible ways.
(b)Flush: five cards of the same suit but different values, for example:
4 combinations of 5 from a set of 13(can be all spades, all diamonds, and hearts or all clubs). So
So 5148 possible ways.
(c)Full house: A three of a kind and a pair, for example:
4 combinations of 3 from a set of 13(three of a kind ,c an be all possible kinds).
3 combinations of 2 from a set of 13(the pair, cant be the kind chosen for the trio, so 3 combinations). So
So 1378 possible ways.
(d)Four of a kind: Four cards of the same value, for example:
4 combinations of 4 from a set of 13(four of a kind, can be all spades, all diamonds, and hearts or all clubs).
1 from the remaining 39(do not involve the kind chosen above). So
So 2899 possible ways.