Computation of the probability to strike the jackpot prize by betting on System 7?

TOTO is a Singapore Lottery. 6 numbers are drawn at random from the numbers 1 to 45. If all the 6 numbers are matched, you won the Jackpot prize. The numbers drawn are not repeated and the sequence is not important. Besides the ordinary 6 numbers bet, there are another method for betting named System Bet. For example, a System 7 bet is a selection of 7 numbers but the winning numbers for the Jackpot still remaining 6 numbers. Off course, we need to pay higher price for this way for betting. What is the probability to strike the Jackpot prize if System 7 Bet is selected?

Probability of System 7 Bet = C(39,1) / C(45,6) = 1 / 208,847.

Please show the detail computation steps if the above wrong. Why?

Relevance
• Wal C
Lv 6

Probability of winning a system 6 bet = 1/45C6

= 1/8,145,060

A system 7 has 7C6 different combinations of 6 numbers ie 7 system 6 combinations (that is why it costs 7 times a system 6 ticket)

So probability of winning = 7/8,145,060 ( = 1/1,163,580)

Source(s): Me ;^))