A) 2/7
B) 12/49
C) 32/343
D) None of these
Correct Answer: D
Solution :
[d] 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 \[(21)(14)/{{7}^{4}}=6/49.\]
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