To form first group of 10 participants you have [tex] C_{40}^{10} [/tex] ways. After that only 30 volunteers left and to form second group of 10 participants you have [tex] C_{30}^{10} [/tex] ways. After forming second group 20 volunteers left and to form third group of 10 participants you have [tex] C_{20}^{10} [/tex] ways. At last, 10 volunteers left and to form fourth group of 10 participants you have [tex]C_{10}^{10}[/tex] ways.
Use product rule to count the total number of possible ways:
[tex] C_{40}^{10}\cdot C_{30}^{10} \cdot C_{20}^{10}\cdot C_{10}^{10} =\dfrac{40!}{10!\cdot 30!} \cdot \dfrac{30!}{10!\cdot 20!} \cdot \dfrac{20!}{10!\cdot 10!} \cdot \dfrac{10!}{10!\cdot 0!} =\dfrac{40!}{(10!)^4} [/tex]