Combinations question (1 Viewer)

[enigma_1]

Question 1:
In how many ways can 4 letters of the letters of the word TOMATOES be selected? I'm struggling to grasp the worked solutions, anyone have any idea?

Answer: 36 ways


Question 2:
In the game of lotto, players select 6 winning numbers from a total of 44 numbers, ranging from 1 to 44. what is the probability that the six winning numbers contain multiples of 3, 5 or 7?
(Is there a faster way of doing this?)

Answer: 1311/91676

Thanks in advance

 

[Kurosaki]

Question 1:
In how many ways can 4 letters of the letters of the word TOMATOES be selected? I'm struggling to grasp the worked solutions, anyone have any idea?

Answer: 36 ways


Question 2:
In the game of lotto, players select 6 winning numbers from a total of 44 numbers, ranging from 1 to 44. what is the probability that the six winning numbers contain multiples of 3, 5 or 7?
(Is there a faster way of doing this?)
Answer: 1311/91676

Thanks in advance

For the first one with TOMATOES, take cases
Case 1- 2 ts and 2 os. There is only one way for this to occur
Case 2- one pair and two different letters, choose a pair - 2 ways.
There are then 5 letters left to choose from, 5C2. Multiplying by 2, 20 ways.
Case 3- all different letters, then simply 6c4=15.
Adding, 36

 

[braintic]

Question 2:

From the numbers 1-44, there are 23 numbers which are multiples of 3, 5 or 7.
So you are choosing 6 numbers from 23.

The answer is 23C6 / 44C6, which gives your answer.