General Brazilian
selecionar aleatoriamente
most common usage throughout Brazil
São Paulo
selecionar aleatoriamente / escolher ao acaso
both forms are widely used
Rio de Janeiro
selecionar aleatoriamente / tirar na sorte
informal variant 'tirar na sorte' (draw by luck) is common
Portugal
seleccionar aleatoriamente / escolher ao acaso
note the Portuguese spelling 'seleccionar'; both forms equally used