The probability that a particular student will get Grade A is given by,

Pr(Of a getting A for a particular student)= (MC(M-3))*(1/N)^(M-3)*(1/(N-1))^3+(MC(M-2))*(1/N)^(M-2)*(1/(N-1))^2+(MC(M-1))*(1/N)^(M-1)*(1/(N-1))^1+(MCM)*(1/N)^M*(1/(N-1))^0.

Now Pr(a particular student does not get A)=1-Pr(He/She gets A).

Also Pr(out of 200 students atleast one gets A)=1-Pr(none gets A).

Since all events are independent,

pr(None gets A)={1-{(MC(M-3))*(1/N)^(M-3)*(1/(N-1))^3+(MC(M-2))*(1/N)^(M-2)*(1/(N-1))^2+(MC(M-1))*(1/N)^(M-1)*(1/(N-1))^1+(MCM)*(1/N)^M*(1/(N-1))^0]}^200.

So required probability=1-{1-{(MC(M-3))*(1/N)^(M-3)*(1/(N-1))^3+(MC(M-2))*(1/N)^(M-2)*(1/(N-1))^2+(MC(M-1))*(1/N)^(M-1)*(1/(N-1))^1+(MCM)*(1/N)^M*(1/(N-1))^0]}^200.

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