if in a hall there are 10 randomly selected students then how many numbers of ways are there such that of them have different birthday. assume that all of then have their birthday in non leap years?
Answers
Answer:
3628800
Step-by-step explanation:
10*9*8*7*6*5*4*3*2*1
Given : in a hall there are 10 randomly selected students
To find : numbers of ways such that all of them have different birthday.
Solution:
in a hall there are 10 randomly selected students
all of then have their birthday in non leap years
=> Days in a years = 365
numbers of ways are there such that all of them have different birthday
=> we need to select 10 Birthdays out of 365 and those 10 birthdays can be arranged in 10! ways
= ³⁶⁵C₁₀ * 10 ! or ³⁶⁵P₁₀
= 365! / 355!
= (365)(364)(363)(362)(361)(360)(359)(358)(357)*356)
numbers of ways are there such that all of them have different birthday = 365! / 355!
numbers of ways are there such that none of them have different birthday
=> 1 birthday has to be selected out of 365
Hence 365 Ways
numbers of ways are there such that none of them have different birthday = 365
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