MAT3707 ASSIGNMENT 3 SOLUTIONS 2023 UNISA DISCRETE MATHEMATICS AND COMBINATORICS

MAT3707
ASSIGNMENT 3
SOLUTIONS 2023
Unique number: **********
DUE DATE: 18 AUGUST 2023
DISCRETE
MATHEMATICS:
COMBINATORICS




Page 1 of 18

,SOLUTION:




SOLUTION:
At most n means either

• No 0’s which happens in (64
0
) = 1 way , or
• One 0 which happens in (64
1
) ways , or
• two 0’s which happens in (64
2
) ways , or
• three 0’s which happens in (64
3
) ways , or
• four 0’s which happens in (64
4
) ways , or

• ……

• n 0’s which happens in (64
n
) ways
• These cases are non-overlapping, so we may use the addition principle: the
total is

1+ (64
1
) + (64
2
) + (64
3
) + (64
4
) + …+ (64
n
)




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, SOLUTION:




(b) containing at least one 5




SOLUTION:




Page 3 of 18