Three cards are numbered 2,3 and 4. List all the possible 3-digit numbers that can be formed when placing the cards on a table next to each other.Find the probability of forming:
(i)the number 234
(ii)an odd number
(iii)an even number
(iv)a number greater than 300
Ans:
The first digit of the 3 digit number can be formed in 3 ways (any of the 3 cards
can be picked).
The second in 2 ways (because once the 1st card is picked, you can pick only from
the remaining 2)
The third in only one way (last card remaining)
So the total number of combinations is 3*2*1 = 6. i.e. 6 numbers can be formed.
Here they are:
234
243
324
342
423
432
i) probability of getting 234 = 1/6 (only one of the 6 numbers is 234)
ii) odd number = 2/6 or 1/3 (2 of the 6 numbers are odd)
iii) even number = 4/6 or 2/3 (4 of the 6 numbers are even)
iv) number > 300 = 4/6 or 2/3 (4 of the 6 numbers are > 300)
Hope this helps :)