In how many ways can $15$ indistinguishable fish be placed into $5$ different ponds, so that each pond contains at least one fish?

given that distribution of 15 identical fish into 5 distinct ponds where each box contains at least one fish.

Number of ways fishes placed in ponds

= $\binom{n-1}{r-1}$=$\binom{14}{4}$ =1001

Hence.Option(A)1001.