Answer:
a)38760
b)5005
c)210
Step-by-step explanation:
Given that
20 identical sticks
We have to 6 of them
a)
The number of choice will be [tex]_{6}^{20}\textrm{c}[/tex].
[tex]_{6}^{20}\textrm{c}=\dfrac{20!}{6!.14!}[/tex]
[tex]_{6}^{20}\textrm{c}=38760[/tex]
b)
The number of choices if no two of the chosen sticks can be consecutive will be [tex]_{6}^{15}\textrm{c}[/tex].
[tex]_{6}^{15}\textrm{c}=\dfrac{15!}{6!9!}[/tex]
[tex]_{6}^{15}\textrm{c}=5005[/tex]
c)
|xx|xx|xx|xx|xx|
Total seven positions are available
So
4-0-0-0-0-0-0 7!/6!=7
3-1-0-0-0-0-0 7!/5!=42
2-2-0-0-0-0-0 7!/2!5!=21
2-1-1-0-0-0-0 7!/2!4!=105
1-1-1-1-0-0-0 7!/4!3!=35
Now by adding all 7+42+21+105+35=210
Answer:
Answer:
a)38760
b)5005
c)210
Given that
20 identical sticks
We have to 6 of them
a)
The number of choice will be .
b)
The number of choices if no two of the chosen sticks can be consecutive will be .
c)
|xx|xx|xx|xx|xx|
Total seven positions are available
So
4-0-0-0-0-0-0 7!/6!=7
3-1-0-0-0-0-0 7!/5!=42
2-2-0-0-0-0-0 7!/2!5!=21
2-1-1-0-0-0-0 7!/2!4!=105
1-1-1-1-0-0-0 7!/4!3!=35
Now by adding all 7+42+21+105+35=210
Step-by-step explanation:
