The two words,as a pronouns,are used to ask for numbers,
but they differ from each other in the following point:

1."多少 duōshao"can be used to ask any numbers,but generally the numbers over ten.
"几jǐ"is usually used to ask for numbers less than ten,
but is not subjectedto the restriction when used to ask for ordinal numbers or collocating with words like“楼lóu",“年nián ”，"天  tiān"and ect.

2."多少duōshao",when used before a noun,can also indicate a large but not precise number.
In this case,the quantifier is usually omitted."几jǐ",when uesd before a noun,can also mean "some","a few",
but the quantifier can not be omitted in this case."多少duōshao
"can aslo be used before uncountable nouns to indicate an uncertain or indefinite quantity,but "几jǐ"can not be used in this way.

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