+0

# Urgent Probability Question

-4
61
14

(a) Count the number of quadruples (a, b, c, d) of nonnegative integers such that 0<= a < b < c < d <= 12.

(b) For this part, we want to count the number of quadruples (a, b, c, d) of nonnegative integers such that  0 <= a <= b <= c <= d <= 12.
Here, some of  a, b, c and d can be equal to each other, so the answer will be different from part (a). Each value a, b, c, d must be between 0 and 12 inclusive. One idea is to count how many times each number appears.

(c) In general, find the number of  k-tuples (a_1, a_2, ... a_k) of nonnegative integers such that
0 <= a_1 <= a_2 <= a_3 <= . . . <= a_k <= n.

Apr 7, 2020

#1
0

Apr 7, 2020
#4
0

I checked the answer to that question and the answerer did not consider 0 as a valid digit, therefore all of his/her answers were based off of 12 instead of 13.

DeSTrOYer303  Apr 7, 2020
#5
0

Yes, it is 13 C 4.... 0 and 12 are included...

tertre  Apr 7, 2020
#6
0

Yeah I just saw that...

HELPMEEEEEEEEEEEEE  Apr 7, 2020
#2
+1

(a): This seems complicated, yet I think 13 C 4 = 715 ways if a is the least, b is the second to least, etc.

Yes, you're right...

Apr 7, 2020
edited by tertre  Apr 7, 2020
#3
+1

There would be 13 integers to choose from right?

So it would be 13 C 4= 715

HELPMEEEEEEEEEEEEE  Apr 7, 2020
edited by HELPMEEEEEEEEEEEEE  Apr 7, 2020
edited by HELPMEEEEEEEEEEEEE  Apr 7, 2020
#7
0

I did get 715 for the first part, and I did not have trouble with that. For part b, I just don't know whether to approach this problem with casework or some sort of counting technique like stars and bars. One of the hints for part b was to approach the problem by designating variables.

DeSTrOYer303  Apr 7, 2020
edited by DeSTrOYer303  Apr 7, 2020
#8
0

For b., if a were 13 then there is one arrangement where all of them are 13, if a were 12 then there are 4 arragements... I wonder if there is a pattern.

HELPMEEEEEEEEEEEEE  Apr 7, 2020
#9
0

There are 10 arrangements if a is 11...

HELPMEEEEEEEEEEEEE  Apr 7, 2020
#10
0

Is there 20 arrangements if a is 10?

DeSTrOYer303  Apr 7, 2020
#11
0

I'm not seeeing any pattern here, so we should probably look for something else...

HELPMEEEEEEEEEEEEE  Apr 7, 2020
#12
+1

I mean the numbers are in order of 3 C 3, 4 C 3, 5 C 3...

DeSTrOYer303  Apr 7, 2020
#13
0

That is a great observation! If that is the pattern, then you should be able to solve the problem from there!

Apr 7, 2020
#14
0

Thanks!

DeSTrOYer303  Apr 7, 2020