(a) Letters and digits that cannot be repeated will be 39,31,20,000.
(b) Letters and digits that can be repeated will be 6.76 × 10⁹.
(c) The letters are nonrepeated consonants and the digits that can be repeated will be 2.35 × 10⁹.
A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.
The serial number on a bill consists of a letter followed by seven digits and then a letter.
A) Letters and digits cannot be repeated. Then the number of ways will be
⇒ 26 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 25
⇒ 39,31,20,000
B) Letters and digits can be repeated. Then the number of ways will be
⇒ 26 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 26
⇒ 6.76 × 10⁹
C) The letters are non-repeated consonants and the digits can be repeated.
⇒ (5 x 10⁷ x 5) + (21 x 10⁷ x 5) + (5 x 10⁷ x 21)
⇒ 0.25 × 10⁹ + 1.05 × 10⁹ + 1.05 × 10⁹
⇒ 2.35 × 10⁹
More about the permutation and the combination link is given below.
#SPJ2
Answer:
408,844,800.
Step-by-step explanation:
(a) There are 26 letters in the alphabet and 10P7 ways of ordering 7 digits.
10P7 = 10!/3! = 604800
The answer is 26* 604800 * 26
= 26^2 * 604800
= 408844800.
m = 1
m = 0
m=-1
Answer:
m=1
Step-by-step explanation:
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Step-by-step explanation:
To find the solution to the inequality 0.125x + 1 - 0.25x < -3, we can simplify and solve for x.
0.125x + 1 - 0.25x < -3
Combining like terms:
-0.125x + 1 < -3
Subtracting 1 from both sides:
-0.125x < -4
Now, to isolate x, we divide both sides by -0.125. However, since we are dividing by a negative number, we need to reverse the inequality sign:
x > -4 / -0.125
Simplifying the division:
x > 32
Therefore, the solution to the inequality 0.125x + 1 - 0.25x < -3 is x > 32.
T = Q – MC
T = Q + MC
T = QMC
T = Q divided by the quantity M times C