How many five​-digit numbers can be formed with the first two digits odd and the last three digits even​?   ​(a) if repetition of digits is​ allowed? ​(b) if repetition of digits is not​ allowed?

Q: How many different numbers can be formed by various arrangements of the six digits 1, 1, 1, 1, 2, 3

A: Please refer to the solution in next step.

Q: Here are the first three stages of a sequence of dots. If we drew each of the first 15 stages, how…

A: The objective of the question is to find the total number of dots in the first 15 stages of a…

Q: Think about the three-digit numbers that can be formed from the digits 1, 2, 3, 4 and 5 without…

A: Solution

Q: How many seven-digit numbers can be formed with the first two digits odd and the last five digits…

A: The total number of digits from 0 to 9 is 10.

Q: How many numbers of four digits can be formed with the digits 0, 1, 2, 3 (repetition of digits being…

A:

Q: Prove: The sum of an odd number of odd numbers must be odd.

A: Let us prove this by induction, that if n is odd and a1,a2,. . .. .an are odd, then ∑i=1nai is odd.…

Q: 692 + 685 + 678 + 671 + ... + 6

A:

Q: How many different three digit numbers can be formed using the digits 9,6,7,8,5 and 4 with…

A: Given digits, 9, 6,7,8,5 and 4 Total numbers of given digits = 6

Q: A state's licese plate has 7 characters. Each character can be a capital letter (A – Z), or a…

A: Number of license plates= (no .of arrangements of 3 capital letters )*(no. of arrangements of 4…

Q: Identify where on the number line 1-1.8 is located. DA ◆◆◆ -14-13 -12 -11 -10 -9-8-7-6-5-4-3-2-1 0 1…

A: identify the point where |-1.8| is located ?

Q: How many three-digit numbers are possible under each condition? (a) The leading digit cannot be zero…

A: We know that 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are digits in the number system.

Q: How many 5–digit (decimal) integers are there with none of the digits repeated?

A:

Q: How many 6-digit numbers have three even and three odd digits? (The first digit cannot be zero.)

A: It is given that a 6-digit number is to be formed which will have three even and three odd digits.…

Q: How many even 4-digit numbers can be formed from the digits 1, 2, 6, 7, and 9 with no repetitions…

A: There is no repetition allowed.. At unit place we have two choices 2 or 6 In 10th place we have…

Q: Until recently, all area codes had a 0 or a 1 as the middle digit and the first digit could not be 0…

A: Given: All area code has 0 or 1 as a middle digit and first digit could not be 0 or 1 and third…

Q: How many 7-digit telephone numbers are possible if the first digit cannot be four and (a) only even…

A: Note: Thank you for the question. As you have posted multiple sub-parts, we have solved the first…

Q: -3, -9, -27, –81, ... a) How do you find the next term?

A: Given that  -3,-9,-27,-81,.... To find the next term

Q: In Connecticut, auto license plates carry 3 digits followed by 3 letters. (Assume the first digit…

A: Since no restrictions are posted it is taken as digits and letters may repeat. Total number of…

Q: How many 7-digit telephone numbers are possible if the first digit cannot be four and (a) only odd…

A: Total digits :  0,1,2,3,4,5,6,7,8,9  7-digit telephone numbers= ?  First digit can not be 4