HELP: Combinations formula

[chronz]

Q:Of the 10 beads in a bag, no two beads are the same color. If 4
beads are to be selected at from the bag, how many di¤erent
groups of 4 beads could be selected?
(A) 40
(B) 80
(C) 120
(D) 210
(E) 420

Explanation:2. D
Explanation: This is a combinations problem. There are 10 beads to
choose from, and we’re looking for of distinct 4-bead subsets. The order doesn’t matter. Plug in n = 10 and k = 4 to the combinations formula:
They do the combinations formula and end up with
10!/4!6! = 10x9x8x7/4x3x2x1 = 10x3x7=210

Link to answer: https://www.gmathacks.com/pdfs/GDT-Apr18 ... ations.pdf

My Question: How do they come up with 10x3x7 from the prior equality, is it a combinations formula trick or division i am not seeing? any explanation of this would be greatly appreciated!

[smohsin]

They just crossed off the numerators by the denominators based on factors. So, 10*9*8*7/4*3*2*1 = 5*3*2*7; multiply 5 and 2 you get 10 and hence left with 10*3*7.