What's the difference between account and count?

[Franssnouf]

Business Idiom in English, Intermediate level

ESL/EFL Test #131 "Ways of approving", question 4

You can ......... on me for support when the next election comes up.

(a) number
(b) count
(c) account
(d) detail

Business Idiom in English, Intermediate level

ESL/EFL Test #131 "Ways of approving", answer 4

You can count on me for support when the next election comes up.

Correct answer: (b) count
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What's the difference between account and count ?

[Mister Micawber]

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The idiom is 'count on' (= rely on, depend on).
.
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Native English teacher at Mister Micawber's