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lilquongohard
02.10.2019 •
Mathematics
There are 20 identical sticks lined up in a row occupying 20 distinct places as follows: · six of them are to be chosen. (a) how many choices are there? (b) how many choices are there if no two of the chosen sticks can be consecutive? (c) how many choices are there if there must be at least two sticks between each pair of chosen sticks?
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Ответ:
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
.
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
Ответ:
very good
Step-by-step explanation:
very good because of we are going back and forth with the simple things like that