A fair die is tossed 10 times. What is the probability that the sum of the scores is 17. Pls explain with workings. Thxs?

The Stars and Bars technique lets you count the number of ways to get this.
You are applying the technique with 10 places, into which you are putting 17 objects (the pips on the die). Each place must have at least 1.

With 1 distributed in each place, that accounts for 10, and so you have 7 more to distribute. You have to eliminated those with more than 6, so you need to count up the ways to get:
8 1 1 1 1 1 1 1 1 1
There are 10C1 = 10 ways to get that.

or
7 2 1 1 1 1 1 1 1 1
There are 10x9 = 90 ways to get that (10 choices for the 7, times 9 choices for the 2.

90+10 = 100 = what we need to subtract from the Stars and Bars formula for k =10-tuples of positive integers adding up to n = 17. That is (n+k-1)C(k-1) = 16C9 = 11440.

11440 - 100 = 11340 is the number of ways to get 17.

There are 6^10 possible sequences of 10 rolls.
11340 / 6^10 = 0.018754%

Another way to do it is to list all possible combinations, and find the number of permutations for each. If you have 10 numbers, and, say, 3 of 1 and 7 of another (like 3 1's and 7 2's), then the number of permutations is 10! / 2!7! = 120.

I did that calculation in Excel, as shown below, and reproduced the number of rolls, 11340. It always increases confidence when you can do a problem 2 different ways and get the same result. I've also posted a link to an explanation of the Stars and Bars method.

You have to know how many possible outcomes exist that gives a sum of 17 out of 10 throws of a 6-sided die. Then divide that by the total number of possible outcomes (6¹⁰).

Doing a little brute-forcing here, I wrote a small computer program to come up with every combination of a sum of 17 with 10 dice rolls and give me a count. The result is:

11340

so:

11340 / 6¹⁰
11340 / 60466176
0.0001875 (rounded to 5 SF)

If there's a less brute-forcey way to know this, I'm not aware, but wouldn't surprise me if there was a way to do that.

For completion, with the minimum amount possible being 10 and the maxmimum amount being 60, here are the number of ways each value can land:

There is 1 way to roll a 10 with 10 dice.
There are 10 ways to roll a 11 with 10 dice.
There are 55 ways to roll a 12 with 10 dice.
There are 220 ways to roll a 13 with 10 dice.
There are 715 ways to roll a 14 with 10 dice.
There are 2002 ways to roll a 15 with 10 dice.
There are 4995 ways to roll a 16 with 10 dice.
There are 11340 ways to roll a 17 with 10 dice.
There are 23760 ways to roll a 18 with 10 dice.
There are 46420 ways to roll a 19 with 10 dice.
There are 85228 ways to roll a 20 with 10 dice.
There are 147940 ways to roll a 21 with 10 dice.
There are 243925 ways to roll a 22 with 10 dice.
There are 383470 ways to roll a 23 with 10 dice.
There are 576565 ways to roll a 24 with 10 dice.
There are 831204 ways to roll a 25 with 10 dice.
There are 1151370 ways to roll a 26 with 10 dice.
There are 1535040 ways to roll a 27 with 10 dice.
There are 1972630 ways to roll a 28 with 10 dice.
There are 2446300 ways to roll a 29 with 10 dice.
There are 2930455 ways to roll a 30 with 10 dice.
There are 3393610 ways to roll a 31 with 10 dice.
There are 3801535 ways to roll a 32 with 10 dice.
There are 4121260 ways to roll a 33 with 10 dice.
There are 4325310 ways to roll a 34 with 10 dice.
There are 4395456 ways to roll a 35 with 10 dice.
There are 4325310 ways to roll a 36 with 10 dice.
There are 4121260 ways to roll a 37 with 10 dice.
There are 3801535 ways to roll a 38 with 10 dice.
There are 3393610 ways to roll a 39 with 10 dice.
There are 2930455 ways to roll a 40 with 10 dice.
There are 2446300 ways to roll a 41 with 10 dice.
There are 1972630 ways to roll a 42 with 10 dice.
There are 1535040 ways to roll a 43 with 10 dice.
There are 1151370 ways to roll a 44 with 10 dice.
There are 831204 ways to roll a 45 with 10 dice.
There are 576565 ways to roll a 46 with 10 dice.
There are 383470 ways to roll a 47 with 10 dice.
There are 243925 ways to roll a 48 with 10 dice.
There are 147940 ways to roll a 49 with 10 dice.
There are 85228 ways to roll a 50 with 10 dice.
There are 46420 ways to roll a 51 with 10 dice.
There are 23760 ways to roll a 52 with 10 dice.
There are 11340 ways to roll a 53 with 10 dice.
There are 4995 ways to roll a 54 with 10 dice.
There are 2002 ways to roll a 55 with 10 dice.
There are 715 ways to roll a 56 with 10 dice.
There are 220 ways to roll a 57 with 10 dice.
There are 55 ways to roll a 58 with 10 dice.
There are 10 ways to roll a 59 with 10 dice.
There is 1 way to roll a 60 with 10 dice.

((1/6)(x¹ + x² + x³ + x⁴ + x⁵ + x⁶))¹⁰
{a one-in-six chance of rolling 1 through 6 (the indices of x) for a total of 10 (over all index) rolls}
= (1/6)¹⁰(x¹⁰ + 10x¹¹ + 55x¹² + 220x¹³ + 715x¹⁴ + 2002x¹⁵ + 4995x¹⁶ + 11340x¹⁷ + ...)
{up to the x¹⁷ term ... as far as we need}

So the probability that the sum of the scores is 17 is 11340(1/6)¹⁰ which expands and simplifies to 35/186624.