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how(^{n}c_{0})^{2}+ (^{n}c_{1})^{2}+ (^{n}c_{2})^{2}+ .......+ (^{n}c_{n})^{2}=^{2n}c_{n}A code word consists of two distinct english alphabets followed by two distinct numbers from 1 to 9.For example, AK47 is a code word. Hpw many such words are there?how many of them will end with an even number

Q.1 How many numbers are there between 100 and 1000 such that every digit is either 2 or 9?

Q.2 In how many ways can the following prizes be given away to a class of 30 students, 1st and 2nd in Maths, 1st and 2nd in physics, 1st in chem and 1st in eng

please explain me these questions and also its answers......

range of function f(x)=

^{7-x}P_{x-3}the no. of flags with 3 strips in order that can be formed using 2 identical red 2 identical white , 2 identical blue isA question paper contains 6 questions ,each having an alternative . The number of ways an xaminer can answer one or more question is?

Let a

_{n}denote the number of all n-digit positive integers formed by the digit 0,1 or both such that no consecutive digit in them are 0. Let b_{n}= The number of such n-digit integers ending with digit 1 and c_{n}= The number of such n-digit integers ending with digit 0.I. Which of the following is correct of:

(a) a

_{17}= a_{16}+ a_{15}(b) c_{17}is not = c_{16}+ c_{15}(c) b

_{17}is not = b_{16}+ c_{16}(d) a_{17}= c_{17}+ b_{16}II. The value of b

_{6}is :(a) 7 (b) 8 (c) 9 (d) 11

(A)81 (B) 100

(C) 64 (D)49

The number of zeros at the end of (127)! is

The total no. of selections of at most n things from 2n+1 different things is found to be 63. find the value of n.

In an examination, a candidate has to pass in each of the 5 subjects. In how many ways can he fail?

In how many ways it is possible to divide six identical green , six identical blue and six identical red among two persons such that each gets equal number of item

5 digit number divisible by 3 is formed using 0 1 2 3 4 6 7 without repitition , total numbers of such numbers are? Pls explain me step wise along with answer.

The total number of ways in which 5 balls of differnet colours can be distributed among 3 persons so that each person gets atleast one ball is :

(A) 75 (B) 150 (C) 210 (D) 243

the no. of different necklaces formed by using 2n identical diamonds and 3 different jewels when exactly 2 jewels are always together -----find the number of positive integral solutions of the equation xyz=210.

A party of 6 is to be formed from 10 boys and 7 girls so as to include 3 boys and 3 girls. In how many different ways can the party be formed if two particular girls refuse to join the same party ?

How many FIVE letter words are formed from the letters of the word INFINITESIMAL ?

Ans given: 22260. Not getting this answer.

I tried as below -

a) All unique

b) 1 double, 4 unique

c) 2 double 3 unique

d) 1 triple, 3 unique (e.g. I I I N F)

e) 1 triple, 1 double, 1 unique (e.g. I I I N N)

9P4+ 2C1 X 8C4 X 5C2 X 3! + 2C2 X 8C3 X 5C4 X 1! + 1 X 8C3 X 5C3 X 2! +1 X 1 X 5C3 X 5C2

= 24460.

Please help to identify the error.

Thanking you.

(a) 4 (b) 5

(c) 6(d) None of these

^{4},in the decimal notation of which all the digits are distinct?pls solve this question by fundamental principle of counting rather than permutations?Q.1 How many numbers are there between 100 and 1000 such that every digit is either 2 or 9?

Q.2 In how many ways can the following prizes be given away to a class of 30 students, 1st and 2nd in Maths, 1st and 2nd in physics, 1st in chem and 1st in eng

please explain me these questions and also its answers......

10 examination papers are arranged in such a way that the best and the worst papers never come together . The number of arrangements is?

If the letters of the word 'daughter ' are to be arranged so that vowels occupy the odd places , then the number..

in an election the number of candidates are 1 more than the number of peoples to be elected . A voter can vote in 254 ways . Howmany candidates are there.

A- 6

B- 7

C- 8

D- 10

Plz ans fast .and dont think that the question is wrong.

And explain also...

Number of ways in which 3 persons throw a normal die to have a total score of 11 is..??

Find the number of ways of selection of one or more letters from AAAABBCCCDEF if the letters A B are selected atleast once

In how many ways can the letters of the word INSURANCE be arranged so that vowels are occupied at even places?

^{9}(c)^{9}C_{2}(d)^{9}P_{2}1. 166674

2.169194

3.166680

4.181434

A. 24

B. 240

C. 480

D. 504

In how many ways we can select 5 cards from a deck of 52 cards, if each selection must include atleast one kingThe letters of the word VICTORY are rearranged in all possible ways and the words thus obtained are arranged as in a dictionary. What is the rank of the given word VICTORY

(a) 15 (b) 10

(c) 20 (d) None of these

(a) 120,6 (b) 720,12

(c) 120,12(d) 720,24

How many numbers greater than a million can be formed with the digits 2,3,0,3,4,2,3?

how many 4-letter code can be formed using the first 10-letters of the english alphabet,if no letter can be repeated?

explain with reason

in how many ways can the letters of the word "INSURANCE' are arranged so that the vowels are never seperate

(a) 30,10 (b) 35,17

(c) 30,20(d) 35,20

A committee of 6 is to be chosen from 10 persons with the condition that if a perticular person A is chosen, then another particular person B must be chosen

Please answer quick!! Thank you

A mint prepares metallic calenders specifying months, dates and days in the form of monthly sheets(one plate for each month).How many types of calenders should it prepare to serve for all the possibilities in the future?

ANSWER: 14