Question

Lottery codes in the format XYZ are to be distributed. If X is an uppercase vowel, Y is an uppercase consonant, and Z can be any single-digit number, including 0, how many lottery codes are possible?

Answer 1

depends if you cound y as a vowel or not

if you don't count it as a vowel then
aeiou, 5

5*21*10=1050 codes



if you count it as a vowel
6*20*10=1200 codes

Answer 2

1050

Explanation:

Lottery codes in the format XYZ

X is an uppercase vowel

Y is an uppercase consonant

Z can be any single-digit number

So, there are 5 vowels.

We need to select 1 vowel from these 5

There 21 consonants.

We need to select 1 consonant from these 21

There are 10 single digit number 9(including 0)

We need to select 1 single digit number from these 10

Now we will use combination to find how many lottery codes are possible

Formula :
`^nC_r= (n!)/(r!(n-r)!)`

No. of lottery tickets are possible:

=
`^5C_1* ^(21)C_1 * ^(10)C_1/tex]</p><p> =  [tex](5!)/(1!(5-1)!)*(21!)/(1!(21-1)!) *(10!)/(1!(10-1)!)`

=
`(5!)/(1!(4)!)*(21!)/(1!(20)!) *(10!)/(1!(9)!)`

=
`(5*4!)/(1!(4)!)*(21*20!)/(1!(20)!) *(10*9!)/(1!(9)!)`

=
`5*21*10`

=
`1050`

Hence 1050 lottery tickets are possible.