Answer :
1. The No. of ways that 3 prizes can award to 44 contestants is 79464
2. The No. of ways that 3 people can be selected from 15 members is 455
3. The No. of ways that a 5-digit password can form is 126
4. The No. of ways that 6 people can stand in a line is 720
Combinations:
In Mathematics, the combination is the process of selecting a number of objects from a group of objects. The combination of selecting 'a' objects from 'n' things in a time without repetition is given by
ⁿCₐ = n!/a!(n - a)!
Permutations:
A permutation number of arrangements of objects in a definite order. The symbol ⁿPₓ is used to denote the number of permutations of n objects, taken x objects at a time.
ⁿPₓ = n!/(n-x)!
Here we have 3 problems and can be solved as shown below
1. In how many ways can first, second, and third prizes be awarded in a contest with 44 contestants?
Number of contestants = 44
Number of priczes = 3 (1st 2nd and 3rd )
Number of ways can first, second, and third prizes are awarded in a contest with 44 contestants = 44 × 43 × 42 = 79464
2. How many ways can a committee of 3 people be selected from a club that has 15 members?
Number of people = 15
The number of people who can be chosen at a time = 3
The number of ways can a committee of 3 people be selected from a club that has 15 members = 15!/3!(15 - 3)!
= 15!/3!(12)!
= 455
3. How many ways can you make a 5-digit password that can be any number (including zero) or letter (not case sensitive)
In mathematics, we have 9 digits i.e 0 to 9
The number of ways to choose a 5-digit password from the set of 10 digits = 9!/5!(9- 5)!
= 9!/5!4!
= 126
4. How many ways can you order 6 people standing in line?
Number of ways that 6 people can stand in a line = 6 ×5 ×4 ×3 ×2
= 720
Learn more about Permutation and combination at
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