probability question?

Question

Five cards are drawn at random from a deck of standard 52 cards. Find the probability that:

At least one card from each suit is drawn, which means at least one heart, one diamond, one club, and one spade are drawn.

Answer 1

One card from each suit is drawn and a second card is drawn from one of the suits.

P(4 suits) = (4C1)(13C2)(13C1)³ / (52C5)

P(4 suits) = 4*(13*12/2)*13³ / 2,598,960

P(4 suits) = 685,464 / 2,598,960

P(4 suits) = 2,197 / 8,330 = 0.2637455