An english school and a vernacular school are both under one superintendent. suppose that the superintendentship, the four teachership of english and vernacular school each; are vacant, if there be altogether 11 candidates for the appointments, 3 of whom apply exclusively for the superintendentship and 2 exclusively for the appointment in english school, the no. of ways in which the different appointments can be of is?

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Badiuddin askIITians.ismu Expert · Answer

Dear jee king

superitendent position can be filled by in ³C1 ways

now we have 8 candidate and 8 position vacant so all shuld be selected

2 person who apply exclusively for english can be selected in 1 ways

and out of 6 , 2 are appointed for english in ⁶C2 ways

and rest 4 are appointed for vernacular in 1 way

so total ways = 3*1*15*1 =45

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Wajahat Khan · Answer

Yes the total number of ways is 45. But u r forgetting the internal arrangenent of the 8 teachers. The answer will be 45 * 4! * 4! i.e. 25920

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