  Even though strongly correlated systems are abundant, only a few exceptional
cases admit analytical solutions. In this paper we present a large class of
solvable systems with strong correlations.. We consider a set of $N$
independent and identically distributed (i.i.d) random variables $\{X_1,\,
X_2,\ldots, X_N\}$ whose common distribution has a parameter $Y$ (or a set of
parameters) which itself is random with its own distribution. For a fixed value
of this parameter $Y$, the $X_i$ variables are independent and we call them
conditionally independent and identically distributed (c.i.i.d). However, once
integrated over the distribution of the parameter $Y$, the $X_i$ variables get
strongly correlated, yet retaining a solvable structure for various
observables, such as for the sum and the extremes of $X_i$'s. This provides a
simple procedure to generate a class of solvable strongly correlated systems.
We illustrate how this procedure works via three physical examples where $N$
particles on a line perform independent (i) Brownian motions, (ii) ballistic
motions with random initial velocities, and (iii) L\'evy flights, but they get
strongly correlated via {\it simultaneous resetting} to the origin. Our results
are verified in numerical simulations. This procedure can be used to generate
an endless variety of solvable strongly correlated systems.
