Question

We have 1,2,3,4,5,6,7,8,a,b,c,d,e,f

the numbers and letters are in order. How many permutations (arrangements) are there in a way that the order is maintained for numbers and the order is maintained for letters? Explain.

Answer #1

Number of permutations possible in a way that the order is
maintained for numbers and the order is maintained for letters =
= **3003**

Order for numbers is maintained means the numbers can be arranged in ascending order only i e. 1,a,2,3,4,b,5,6,7,c,8

Order for letter is maintained means the letters can be arranged only such that the alphabets (from a-z) always occurs first

We have 8 + 6 = 14 characters

These 14 characters needs to be placed in 14 spots

We select any of the 8 spots out of these 14 and place the numbers 1-8 in the ascending order of the spots.

How many permutations of the set {A, B, C, D, E, F, G, H}
a) Contain the string DEF?
b) Contain the strings ABE and EFG?
c)Have D next to C?
d) Contain the strings DCB and BAD?

Permutations---------
In how many distinct ways can all the letters of the word
UNBELIEVABLE be arranged amongst themselves if
a) there are no restrictions?
b) the arrangement begins with the letters I V A, in that
order?
c) the arrangements must begin and end with a consonant?

Let S = {a,b,c,d,e,f,g} and let T = {1,2,3,4,5,6,7,8}.
a. How many diﬀerent functions are there from S to
T?
b. How many diﬀerent one-to-one functions are there from S to
T?
c. How many diﬀerent one-to-one functions are there from T to
S?
d. How many diﬀerent onto functions are there from T to
S?

How many ways can we order the letters in SEVENTEEN? (Hint: Not
all of the letters are distinct, so the plain permutations formula
does not apply.)

how many distinguishable permutations of letters are possible
using the letters in the word maryland?
A. 20,160
B. 5,040
C. 40,320
D. 80,640

How
many permutations of the letters in the word STAT can you
have?

Consider permutations of the 26-character lowercase alphabet
Σ={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}.
In how many of these permutations do
a,b,c occur consecutively and in that
order?
In how many of these permutations does a appear before
b and b appear before c?

Let letters A,B,C,D,E,F,G be used to form strings of length 4.
How many strings of length 4 with repetitions contain A and B. How
about without repetitions?

Find the number of permutations of a, b, c, d, e, f, g and h
containing no piece ab, or cd, or acb.

The letters of the word “PROBLEM” are arranged in a random
order.
a. How many different arrangements are possible?
b. How many arrangements will start with “OE” or “EO”?
c. How many start with "M" and end with "P"?

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