## Pandigital Primes

A \((1,k)\)-pandigital integer is any number which contains all the digits from \(1\) to \(k\) exactly once each. A \((0,k)\)-pandigital integer is any number which contains all the digits from \(0\) to \(k\) exactly once each. We are interested in counting how many \((1,k)\)-pandigital prime numbers exist.

Part A | How many \((1,7)\)-pandigital prime numbers are there? | |
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Part B | How many \((0,7)\)-pandigital prime numbers are there? |

## Poker Hands

In the game of Poker, Ross has been deal 5 cards from a standard deck of 52 playing cards. We are interested in how many ways Ross' opponent could be dealt a hand of greater value than Ross' hand, from the remaining 47 cards in the deck.

Part A | If Ross' hand is \((KC, KD, KH, KS, 7H)\), then how many possible winning hands could Ross' opponent be dealt? | |
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Part B | If Ross' hand is \((2C, 4C, 7D, 8S, AS)\), then how many possible winning hands could Ross' opponent be dealt? |