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junior college 1 | H1 Maths
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Heya! Im stuck at question 27 (b) and (c)... id appreciate it if someone could help me out. Thanks in advance! =)
Date Posted: 4 years ago
Views: 481
(b) 16
(c) 6
?
(c) 6
?
b)
Number of choices for each region = 2
So
Number of ways to choose the first representative from region 1 = 2
Number of ways to choose the 2nd representative from region 2 = 2
Number of ways to choose the 3rd representative from region 3 = 2
Number of ways to choose the 4th representative from region 4 = 2
Total number of ways = 2 x 2 x 2 x 2 = 16
Number of choices for each region = 2
So
Number of ways to choose the first representative from region 1 = 2
Number of ways to choose the 2nd representative from region 2 = 2
Number of ways to choose the 3rd representative from region 3 = 2
Number of ways to choose the 4th representative from region 4 = 2
Total number of ways = 2 x 2 x 2 x 2 = 16
If you list them out it would be like :
1A 2A 3A 4A
1B 2A 3A 4A
1A 2B 3A 4A
1A 2A 3B 4A
1A 2A 3A 4B
1B 2B 3A 4A
1A 2B 3B 4A
1A 2A 3B 4B
1B 2A 3B 4A
1A 2B 3A 4B
1B 2A 3A 4B
1A 2B 3B 4B
1B 2A 3B 4B
1B 2B 3A 4B
1B 2B 3B 4A
1B 2B 3B 4B
Where 1,2,3,4 refer to the region number, A and B refer to the 2 unique sales reps in each region
You might also notice a special symmetry in the cases above : 1 4 6 4 1 (Pascal's triangle)
1A 2A 3A 4A
1B 2A 3A 4A
1A 2B 3A 4A
1A 2A 3B 4A
1A 2A 3A 4B
1B 2B 3A 4A
1A 2B 3B 4A
1A 2A 3B 4B
1B 2A 3B 4A
1A 2B 3A 4B
1B 2A 3A 4B
1A 2B 3B 4B
1B 2A 3B 4B
1B 2B 3A 4B
1B 2B 3B 4A
1B 2B 3B 4B
Where 1,2,3,4 refer to the region number, A and B refer to the 2 unique sales reps in each region
You might also notice a special symmetry in the cases above : 1 4 6 4 1 (Pascal's triangle)
c)
This is even easier.
We need only 2 of the 4 regions.
Once we have picked 2 regions, the total of 4 people in those selected regions would suffice, since we have 4 people exactly to fill the 4 positions.
We do not need to care about the order of those 4 people.
Number of ways to choose 2 regions from 4 regions
= 4C2
= 4! ÷ (4 - 2)! ÷ 2!
= 4! ÷ 2! ÷ 2!
= 24 ÷ 2 ÷ 2
= 6
This is even easier.
We need only 2 of the 4 regions.
Once we have picked 2 regions, the total of 4 people in those selected regions would suffice, since we have 4 people exactly to fill the 4 positions.
We do not need to care about the order of those 4 people.
Number of ways to choose 2 regions from 4 regions
= 4C2
= 4! ÷ (4 - 2)! ÷ 2!
= 4! ÷ 2! ÷ 2!
= 24 ÷ 2 ÷ 2
= 6
See 1 Answer
done
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clear
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(b) Choose One from each region
(c) Since you can only choose 2 region out of the 4, you'll only have 4 people remaining thus the 4C4
(c) Since you can only choose 2 region out of the 4, you'll only have 4 people remaining thus the 4C4
Date Posted:
4 years ago
The 4C4 is not necessary/ is optional.
Having 4 people left for 4 slots/vacancies/positions means the selection is already done.
Having 4 people left for 4 slots/vacancies/positions means the selection is already done.
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