On how many nights may a watch of 4 men be arranged by a security agency from a crew of 16 so that no two watches are identical? On how many of these nights would a particular person be off-duty?

Dear Sarthak

the number of ways in ¹⁶C₄  = 1820 .

When a perticular man is to be always included then we need to select 3 men out of 23.so total ways = ¹⁵C₃ = 455

Regards

Arun (askIITians forum expert)