Use exponential generating functions to determine the following: Suppose we have 15 blue pebbles, 15 grey pebbles and 15 pink pebbles (pebbles of the same colour are indistinguishable). How many ways can we select 15 of the 45 pebbles and arrange them from left to right on a shelf if we must have all three of the following conditions holding. ( ie there is an 'and' between the conditions, not an 'or'.) at least 1 blue pebble. an even number of grey pebbles. an odd number of pink pebbles.