Answer to Question #194174 in Discrete Mathematics for Saoirse lei kjelbe

Question

Solve the following. (35 pts)

1.    How many 3-digit number can be formed from digits 1 – 5 if:

a.   If repetition is allowed? (3 pts)

b.   If repetition is not allowed? (3 pts)

 

2.    How many strings of length 4 can be formed using the letters

COMPUTER if repetitions are not allowed? (3 pts)

 

3.    Out of 17 regions in the country, ten will be chosen to be included in a survey. How many ways of selecting 10 out of 17 regions? (3 pts)

 

4.    Expand the (2𝑥 − 𝑦)³ using binomial coefficient. (14 pts)

 

5.    Find for the coefficient of the following: (3 pts each)

a.   x⁴y³ after the expansion of (x – 2y )⁷

b.   x⁶y⁶ after the expansion of (2x + y )¹²

 

6.    Find the 9^th term of the expression (2x + y )¹² (3 pts)

Answer 1

1.a) 5*5*5=125

1.b) 5*4*3=60

2) 8*7*6*5=1 680

3) $C^{10}_{17}=19448$

4) binomial coefficients:1 3 3 1

$(2x-y)^3=(2x)^3*1+(2x)^2*(-y)*3+(2x)*(-y)^2*3+(-y)^3*1=\\ =8x^3-12x^2y+6xy^2-y^3$

5.a) binomial coefficients: 1 7 21 35 35 21 7 1

$35*(x)^4*(-2y)^3=280 x^4y^3$

5.b) binomial coefficients: 1 12 66 220 495 792 924 792 495 220 66 12 1

$924 *(2x)^6(y)^6=59136 x^6y^6$

6) binomial coefficients: 1 12 66 220 495 792 924 792 495 220 66 12 1

$495 *(2x)^{12-9+1}(y)^{9-1}=495 *(2x)^4(y)^8=7920x^4y^8$