A lottery drawing selects 4 out of 10 numbers (without replacement). If a player can choose four numbers but need only match three to win, what is the player’s probability of winning the lottery?
Number of ways 4 numbers can be drawn from 10 without replacement is 10C4 =210
To win one needs to select at least 3 number from 4 numbers drawn by the lottery. The ways this can be done is
3 number from the 4 drawn by the lottery + 1 number from the remaining six. The count will be 4C3×6C1 = 24
4 number from the 4 drawn by the lottery. The count will be 4C4×6C0 =1
Total count is =24 + 1 = 25
Probability of winning is 25/210 = 5/42.