Answer :
The value of digit 'a' is 2
Combinations:
In mathematics, combination is the method of selecting a set of objects from a given group.
The formula for the combination of 'r' things from the set of 'n' things is given by ⁿC[tex]_{r}[/tex] = n!/r!(n - r)!
Here we have,
The number of cards from a deck is 52
Number of cards dealt at once = 10
The number of distinct (unordered) hands that can be dealt to the player is written as 158a002a4aa
Here we need to find 'a'
From the above formula,
The number of combinations i.e the number of distinct hands that can be dealt to the player = ⁵²C₁₀
= 52!/10!(52 - 10)!
= 52!/10!(42)!
= [ 52× 51× 50× 49× 48× 47× 46× 45× 44× 43 × 42! ] / 10!(42!)
= [ 52× 51× 50× 49× 48× 47× 46× 45× 44× 43 ] / 10!
= 26 × 17 × 5 × 47 × 46 × 11 × 43
= 15820024220 [ which is equal to 158a002a4aa ]
⇒ a = 2
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The complete problem:
In a certain card game, a player is dealt a hand of 10 cards from a deck of 52 distinct cards. The number of distinct (unordered) hands that can be dealt to the player can be written as 158A00A4AA0. What is the digit A?
