MATHS ASSIGNMENT ON PERMUTATION

   

MAT 111

1. THE ANSWERS

1. To solve this question, we can use the formula for the number of ways to arrange n objects in a circle, which is (n-1)!. Therefore, the number of ways to arrange 7 different appetizers in a circular tray is: (7-1)! = 6! = 720
2. To solve this problem, similar to the above question, we also use the formula for the number of ways to arrange n objects in a circle, which is (n-1)!, the number of ways to arrange 8 different charms in a circular bracelet is: (8-1)! = 7! = 5040

So, there are 720 ways to arrange 7 different appetizers in a circular tray and 5040 ways to arrange 8 different charms in a circular bracelet.

 

2. THE ANSWERS

i) To find the number of 4-digit numbers that can be formed using 6 distinct digits, we can use the permutation formula: ⁶P₄ = 6!/(6-4)! = 6x5x4x3 = 360

Therefore, there are 360 ways to form 4-digit numbers using these digits when the digits are distinct.

ii) When the digits are not distinct,

we can use the combination formula: ⁶C₄ = 6!/(4!x(6-4)!) = 15 Therefore, there are 15 ways to form 4-digit numbers using these digits when the digits need not be distinct.

iii) To form a 4-digit number that is even, the last digit must be either 0, 2, 4, 6, or 8.

There are 5 choices for the last digit. The first three digits can be any of the 6 available digits (since 0 is not allowed as the first digit), and they need not be distinct. So, the total number of even 4-digit numbers that can be formed using these digits is: 5 x 6 x 6 x 6 = 1080

Therefore, there are 1080 ways to form 4-digit even numbers using these digits.

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