There are 4 ace cards in a pack of 52 cards, therefore we can choose maximum 4 ace cards.
Case 1: 3 cards of ace and 2 cards out of remaining 4 cards
i.e. 5 cards combinations out of 52 cards = 4C3 × 48C2
= \(\frac{4!}{3!\space1!}\times\frac{48!}{2!\space46!}\)
= \(4\times\frac{48\times47}{2}\)
= 4512
Case 2: 4 cards of ace and 1 card out of 52 remaining cards
i.e. 5 cards combinations out of 52 cards = 4C4 × 48C1
= \(\frac{4!}{4!\space0!}\times\frac{48!}{1!\space7!}\)
= 1 × 48
Hence, total number of combinations are = 4512 + 48
= 4560
