Question 1;

question 1.jpg


Question 2; Marks: 5
Use the Euclidean algorithm to find gcd of (331, 393) (don’t use hand calculation)
Answer:

393=331.1+62
331=62.5+21
62=21.2+20
21=20.1+1
20=1.20+0
Hence GCD(393,331) = 1

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Question 3; Marks: 5
In how many ways can five distinct Sheep and eight distinct goats stand in line if no two Sheep stand together?

Answer: 609,638,400

There are 5 sheep’s and 8 goats.
Arrange the 8 goats in a row. There are 8! Possibilities.
There are now 9 different places where a sheep can be inserted into that row of goats. Select 5 of those 9 places - there's C(9,5) possibilities.
However, the order of sheep’s also matters. There are 5! possible arrangements of the sheep’s.
The answer is:
there are
8! * C(9,5) * 5! = 40320 * 126 * 120 = 609,638,400
possible arrangements