Class 11MathematicsPermutations and CombinationsDefinition of permutation, Number of permutations with or without repetition, Conditional permutations
EasyHow many $3$-digit numbers can be formed from the digits $1, 2, 3, 4,$ and $5$ assuming that repetition of the digits is allowed?
- A$125$
- B$60$
- C$243$
- D$120$
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How many $5$-digit numbers can be formed using the digits $3, 4, 7$ once each and the digit $5$ twice?
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View SolutionIf $n, r$ are two positive integers such that $1 \leq r < n$,then ${ }^{n} P_{r+1} + r^2 { }^{n-1} P_{r-1} + (r+1) { }^{n-1} P_{r} + r { }^{n-1} P_{r-1} =$
How many $4$-digit odd numbers can be formed using the digits $0, 1, 2, 3, 5, 7$ if repetition of digits is allowed?
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View SolutionEvaluate $4! - 3!$
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View SolutionHow many words can be formed by arranging the letters of the word $MISSISSIPPI$ such that no two $S$ are together?
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