(1). How many strings can be formed by ordering the letters ABCDE subject to the condition that the string contains either the substring AE or the substring EA or both?

(2). In how many ways can five distinct Martians and five distinct Jovians wait in line?

(3). A six-person committee composed of Alice, Ben, Connie, Dolph, Egbert, and Francisco is to select a chairperson, secretary, and treasurer. How many selections are there in which Dolph is an officer and Francisco is not an officer?

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