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In how many ways can we select any $4$ letters from the word $CORGOO$?

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The number of $4$-digit numbers without repetition that can be formed using the digits $1, 2, 3, 4, 5, 6, 7$ in which each number has two odd digits and two even digits is:

Everybody in a room shakes hands with everybody else. The total number of handshakes is $45$. The total number of persons in the room is

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