• (a) is correct.
• First of all, partner’s 3♠ is not precisely defined. Partner could have a full-blooded 3♠ bid that he would have made if East-West had kept quiet. Or he could have been forced to stretch a little to show his spade support because of the opposing intervention.
• Let’s start with Hand (c). This hand has become truly fabulous because partner appears to have a void heart (assuming East-West have nine hearts to bid to the nine-trick level). You have two fits and can expect 6♠ to be an easy make with far fewer points than normal for a small slam (you are playing with a 30-point pack: the opposing 10 points will take no tricks). And note that there’s little point in bidding 4NT to ask for aces, as partner rates to have a void (heart).
• Hand (b) is interesting. You have the values for game, but why not suggest 3NT, as your hearts will provide two stoppers facing partner’s presumed singleton. There are countless hands where 4♠ will lose four tricks whilst 3NT will make.
• That leaves Hand (a): you have lots of points, but the heart holding is very bad for slam (two fast losers) plus the shape is relatively barren. Settle for 4♠..

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