In the 6/55 lottery game, a player picks six numbers from 1 to 55. How many different choices does the player have if repetition is not allowed? Note that the order of the numbers is not important.
Accepted Solution
A:
Answer: 28989675 Step-by-step explanation:The number of ways to choose r things out of n things ( if order doesn't matter) is given by :_[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]Given : In the 6/55 lottery game, a player picks six numbers from 1 to 55.Then , the number of ways to choose 6 numbers out of 55 is if repetition is not allowed :[tex]^{55}C_6=\dfrac{55!}{6!(55-6)!}\\\\=\dfrac{55\times54\times53\times52\times51\times49!}{6\times5\times4\times3\times2\times1\times49!}\\\\=\dfrac{55\times54\times53\times52\times51}{6\times5\times4\times3\times2\times1}\\\\=28989675[/tex]Hence, the player have 28989675 choices.