Answer:
Option D 6 is the answer.
Step-by-step explanation:
the given points are A, D, C and B. If each point in the diagram can act as end points, we have to calculate number of distinct line segments formed.
This ca be calculated in two ways.
(1) We will form the line segments
AB, AC, AD, BC, BD, DC
Therefore 6 segments can be formed.
(2) By combination method
Number of segments = ![^{4}C_{2}](https://tex.z-dn.net/?f=%5E%7B4%7DC_%7B2%7D)
= ![\frac{4!}{2!2!}=\frac{4\times 3\times 2\times 1}{(2\times 1)\times (2\times 1)}](https://tex.z-dn.net/?f=%5Cfrac%7B4%21%7D%7B2%212%21%7D%3D%5Cfrac%7B4%5Ctimes%203%5Ctimes%202%5Ctimes%201%7D%7B%282%5Ctimes%201%29%5Ctimes%20%282%5Ctimes%201%29%7D)
= ![\frac{4\times 3}{2\times 3}=\frac{12}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Ctimes%203%7D%7B2%5Ctimes%203%7D%3D%5Cfrac%7B12%7D%7B2%7D)
= 6
Option D 6 is the answer.
Answer:
x< -64
Step-by-step explanation:
hope this helps ;)
Answer:
12870ways
Step-by-step explanation:
Combination has to do with selection
Total members in a tennis club = 15
number of men = 8
number of women = 7
Number of team consisting of women will be expressed as 15C7
15C7 = 15!/(15-7)!7!
15C7 = 15!/8!7!
15C7 = 15*14*13*12*11*10*9*8!/8!7!
15C7 = 15*14*13*12*11*10*9/7 * 6 * 5 * 4 * 3 * 2
15C7 = 15*14*13*12*11/56
15C7 = 6,435 ways
Number of team consisting of men will be expressed as 15C8
15C8 = 15!/8!7!
15C8 = 15*14*13*12*11*10*9*8!/8!7!
15C8 = 15*14*13*12*11*10*9/7 * 6 * 5 * 4 * 3 * 2
15C8 = 6,435 ways
Adding both
Total ways = 6,435 ways + 6,435 ways
Total ways = 12870ways
Hence the required number of ways is 12870ways
Answer:
D
Step-by-step explanation:
You are going to roll two dice.
If you roll one die, then there are 6 possible outcomes: ![1, 2, 3, 4, 5, 6](https://tex.z-dn.net/?f=1%2C%202%2C%20%203%2C%204%2C%205%2C%206)
If you roll two dice, then there are
possible outcomes:
![\begin{array}{cccccc}1-1&1-2&1-3&1-4&1-5&1-6\\ \\2-1&2-2&2-3&2-4&2-5&2-6\\ \\3-1&3-2&3-3&3-4&3-5&3-6\\ \\4-1&4-2&4-3&4-4&4-5&4-6\\ \\5-1&5-2&5-3&5-4&5-5&5-6\\ \\6-1&6-2&6-3&6-4&6-5&6-6\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bcccccc%7D1-1%261-2%261-3%261-4%261-5%261-6%5C%5C%20%5C%5C2-1%262-2%262-3%262-4%262-5%262-6%5C%5C%20%5C%5C3-1%263-2%263-3%263-4%263-5%263-6%5C%5C%20%5C%5C4-1%264-2%264-3%264-4%264-5%264-6%5C%5C%20%5C%5C5-1%265-2%265-3%265-4%265-5%265-6%5C%5C%20%5C%5C6-1%266-2%266-3%266-4%266-5%266-6%5Cend%7Barray%7D)
Here the first number is the number rolled on the first die, the second number is the number rolled on the second die.