100 points question...
ans--6.8121×10^8
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Answers
Hey there!
Q. In how many ways can the following prizes be given away to a class of 30 students, first and second in Mathematics, first and second in Physics, first in Chemistry and first in English?
Solution:
Number of First Prizes = 4 (i.e Maths, Physics, Chemistry, English)
Number of Second Prizes = 2 (i.e Maths, physics)
First Prize in Mathematics can be distributed to 30 students in 30 ways.
Likewise, 1st prize in Physics can be distributed to 30 students in 30 ways.
First Prize in Chemistry can be distributed to 30 students in 30 ways.
First Prize in Physics can be distributed to 30 students in 30 ways.
Number of ways(only for 1st prize):
= 30 * 30 * 30 * 30 = 810000 = 8.1 * 10^5
Now,
1 student must have got 1st prize in Maths and Physics.
No. of students left in each subject = 29.
Then,
2nd Prize in Mathematics can be distributed to 29 students in 29 ways.
2nd Prize in Physics can be distributed to 29 students in 29 ways.
Number of ways(only for 2nd prize):
= 29 * 29 = 841
Total number of ways of Prize distribution:
= 8.1 * 10^5 * 841 = 6812.1 * 10^5 = 6.8121* 10^8
Answer :
Number of First Prizes = 4 (i.e Maths, Physics, Chemistry, English)
Number of Second Prizes = 2 (i.e Maths, physics)
First Prize in Mathematics can be distributed to 30 students in 30 ways.
Likewise, 1st prize in Physics can be distributed to 30 students in 30 ways.
First Prize in Chemistry can be distributed to 30 students in 30 ways.
First Prize in Physics can be distributed to 30 students in 30 ways.
Number of ways(only for 1st prize):
= 30 * 30 * 30 * 30 = 810000 = 8.1 * 10^5
Now,
1 student must have got 1st prize in Maths and Physics.
No. of students left in each subject = 29.
Then,
2nd Prize in Mathematics can be distributed to 29 students in 29 ways.
2nd Prize in Physics can be distributed to 29 students in 29 ways.
Number of ways(only for 2nd prize):
= 29 * 29 = 841
Total number of ways of Prize distribution:
= 8.1 * 10^5 * 841 = 6812.1 * 10^5 = 6.8121* 10^8 __________ (Ans.)
Hope it helps.
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