Gate Exam

A drawer holds 4 red hats & 4 blue hats.what is the probability of getting exactly three red hats or exactly three lue hats when taking out 4 hats randomly out of the drqwer & immediately returning every hat to the drawer before taking out the next?

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Gate Other Question

using the transformation x=r cosθ and y=r sinθ,find the singular solutionof the differential equation x+py=(x-y)(p2+1)½ where p=dy/dx Mr &mrs smith have invited 9 of their friends & their spouses for a party at the waikki beach resort.they started for a group photograph.if Mr.smith never stands next to mrs smith(as he says they are always together otherwise).how many ways the group can be arranged in a row for the photograph?