How many different hands can be dealt?

A 40-card Spanish deck can produce 91,390 different 4-card hands, as in Mus (mus), and 9,880 3-card hands, as in Brisca (brisca). If you deal 6 cards, as in Guiñote (guinote), there are more than 3.8 million possible hands; with 10, as in four-player Tute (tute), the figure exceeds 847 million.

How to work it out

We use what are called ‘combinations’: the number of ways to choose a group of cards without taking their order into account. For 4 cards out of 40, multiply 40 × 39 × 38 × 37 and divide by 4 × 3 × 2 × 1. The result is 91,390.

Why doesn’t the order matter?

Because when you look at your hand, it doesn’t matter which card arrived first. Having the ace and the king is the same as having the king and the ace.

At a glance

• 3 cards: 9,880
• 4 cards: 91,390
• 5 cards: 658,008
• 6 cards: 3,838,380
• 10 cards: 847,660,528

A number to impress your friends

If you played one hand of Mus every minute, without stopping, it would take you more than two months to see every possible hand. And that assumes none were repeated, which wouldn’t happen. You’ll find more numbers like these in how many combinations a deck of cards has.