Conditional probability maybe

At a rough guess
9/15 x 8/14 x 7/13 x......x 3/9
(but no guarantee )

I came up with:

Ways to pick only questions that he can answer = 9x8x7x6x5x4x3 / 7! (because the order doesn't matter)

Total ways to pick 7 questions =15x14x13x12x11x10x9 / 7!

Prob is first divided by the second, which reduces to your answer after eliminating the common factor of 7!.

I explained my answer to my daughter who doesn't understand it and claims there must be a simpler or more intuitive answer

Its like picking 7 white balls from a bag of 9 white plus 6 black.
The probability of the first white is 9/15, that of the second is 8/14 and so on.
The combined probability (first AND second AND...) is found by multiplying.

Makes sense to me. Thanks.