Probability Question 353
Question: If the papers of 4 students can be checked by any one of the 7 teachers, then the probability that all the 4 papers are checked by exactly 2 teachers is
Options:
A) 2/7
B) 12/49
C) 32/343
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
The total number of ways in which papers of 4 students can be checked by seven teachers is $ 7^{4}. $
The number of ways of choosing two teachers out of 7 is $ ^{7}C_2. $ The number of ways in which they can check four papers is $ 2^{4}. $
But this includes two ways I which all the papers will be checked by a single teacher.
Therefore, the number of ways in which 4 papers can be checked by exactly two teachers is $ 2^{4}-2=14. $
Therefore, the number of favourable ways is $ {{(}^{7}}C_2)(14)=(21)(14). $
Thus, the required probability is $ (21)(14)/7^{4}=6/49. $
BETA
