A single die is rolled four times.

What is the probability that the numbers that come up will be in ascending order (not necessarily strictly ascending, but never a lower number after a higher)?

Intended to be solved without a computer.

1. How did you arrive at the sequence a(1) = 6; a(2) = 21; etc.

**I trust it was adequately explained in my previous**

comment.

2. Was the source Sloane's OEIS?

**No, I Just looked up a DIAGONAL in Pascal triangle**

and from the locations where 1,6,21,56.126,252 etc

appeared deduced that there are

a(n)=C(n+k-1,n) ascending sequences, n being number of throws using a k-sided dice.

Then i've validated the formula for k=1 ==>** a(n)=1 and for n=4 k=3 listed all 15 outcomes.**

Following your enquiry I visited SLOANE & found similar,

-not exactLY THE SAME= formula with another offset, did not bother to study it since no recursion or generating function was presented there.

3. Was a computer used in looking this up?

**Neither computer, worksheet nor calculator were used**

Primo

**, it was**
**Intended to be solved without a computer.**

and secondo , **I always prefer the BRAIN, i.e. analytical approach.**

**.....**