Simple Applications
Permutation and Combination

119302 The number of all three digit even numbers such that, if 5 is one of the digits, then next digit is 7 is

1 360
2 365
3 370
4 375
Permutation and Combination

119303 The sum of all possible numbers that can be formed by using the digits is \(2,3,5,7\) without repetition of digits is

1 \(17 \times \frac{10^4-1}{9}\)
2 \(33 \times 34 \times 101\)
3 \(6 \times \frac{10^3-1}{9}\)
4 \(33 \times 35 \times 1001\)
Permutation and Combination

119304 If \(P(n)\) is a statement such that \(P(3)\) is true. Assuming \(P(k)\) is true \(\Rightarrow P(k+1)\) is true for all \(k \geq 3\), then \(P(n)\) is true

1 for all \(\mathrm{n}\)
2 for \(\mathrm{n} \geq 3\)
3 for \(\mathrm{n} \geq 4\)
4 None of these
Permutation and Combination

119305 The number of natural numbers less than 1000 in which no digit is repeated is

1 729
2 738
3 792
4 836
Permutation and Combination

119302 The number of all three digit even numbers such that, if 5 is one of the digits, then next digit is 7 is

1 360
2 365
3 370
4 375
Permutation and Combination

119303 The sum of all possible numbers that can be formed by using the digits is \(2,3,5,7\) without repetition of digits is

1 \(17 \times \frac{10^4-1}{9}\)
2 \(33 \times 34 \times 101\)
3 \(6 \times \frac{10^3-1}{9}\)
4 \(33 \times 35 \times 1001\)
Permutation and Combination

119304 If \(P(n)\) is a statement such that \(P(3)\) is true. Assuming \(P(k)\) is true \(\Rightarrow P(k+1)\) is true for all \(k \geq 3\), then \(P(n)\) is true

1 for all \(\mathrm{n}\)
2 for \(\mathrm{n} \geq 3\)
3 for \(\mathrm{n} \geq 4\)
4 None of these
Permutation and Combination

119305 The number of natural numbers less than 1000 in which no digit is repeated is

1 729
2 738
3 792
4 836
Permutation and Combination

119302 The number of all three digit even numbers such that, if 5 is one of the digits, then next digit is 7 is

1 360
2 365
3 370
4 375
Permutation and Combination

119303 The sum of all possible numbers that can be formed by using the digits is \(2,3,5,7\) without repetition of digits is

1 \(17 \times \frac{10^4-1}{9}\)
2 \(33 \times 34 \times 101\)
3 \(6 \times \frac{10^3-1}{9}\)
4 \(33 \times 35 \times 1001\)
Permutation and Combination

119304 If \(P(n)\) is a statement such that \(P(3)\) is true. Assuming \(P(k)\) is true \(\Rightarrow P(k+1)\) is true for all \(k \geq 3\), then \(P(n)\) is true

1 for all \(\mathrm{n}\)
2 for \(\mathrm{n} \geq 3\)
3 for \(\mathrm{n} \geq 4\)
4 None of these
Permutation and Combination

119305 The number of natural numbers less than 1000 in which no digit is repeated is

1 729
2 738
3 792
4 836
Permutation and Combination

119302 The number of all three digit even numbers such that, if 5 is one of the digits, then next digit is 7 is

1 360
2 365
3 370
4 375
Permutation and Combination

119303 The sum of all possible numbers that can be formed by using the digits is \(2,3,5,7\) without repetition of digits is

1 \(17 \times \frac{10^4-1}{9}\)
2 \(33 \times 34 \times 101\)
3 \(6 \times \frac{10^3-1}{9}\)
4 \(33 \times 35 \times 1001\)
Permutation and Combination

119304 If \(P(n)\) is a statement such that \(P(3)\) is true. Assuming \(P(k)\) is true \(\Rightarrow P(k+1)\) is true for all \(k \geq 3\), then \(P(n)\) is true

1 for all \(\mathrm{n}\)
2 for \(\mathrm{n} \geq 3\)
3 for \(\mathrm{n} \geq 4\)
4 None of these
Permutation and Combination

119305 The number of natural numbers less than 1000 in which no digit is repeated is

1 729
2 738
3 792
4 836