we assume an unlimited supply of cameras, so that the probability of buying a camera made in Japan is 22% for any single purchase throughout the entire day

1/0.22 = 4.545

there are 1 in 4.545 ways to buy a camera from Japan

there are 20! different iterations in which 20 different cameras can be purchased

we calculate the different iterations, 'p', for which up to 5 Japanese cameras could be purchased (hence, 15 not made in Japan were purchased):

p = 20*0.4545 + 20*19*4.545^2 + 20*19*18*4.545^3 + 20*19*18*17*4.545^4 + 20*19*18*17*16*4.545^5

(p)/(20! * 0.4545^20) = 0.0106

the probability is approximately 0.0106, or about a 1% probability