PnC 7-DERANGEMENTS & SPECIAL CASES || Quantitative Aptitude || CAT 2021 || 25 October

A shop owner has an unlimited supply of 9 different types of flowers. If a customer asks for a six flower arrangement such that the arrangement should start and end with the same type of flower and 3rd flower should be green which is one of the variety that shopkeeper have, then in how many ways the arrangement can be made by the shop owner? (TITA)

p, q, r and s are one of the digits 1, 7, 5 or 6, with each digit used only once. How many different values of p × s + r × q can be obtained?

An executive wrote five letters to five people A, B, C, D, E and asked his secretary to place them in five envelopes also marked A, B, C, D, E. The secretary, however, placed the letters at random into the envelopes such that each envelope received exactly one letter. Then the number of arrangements in which exactly two letters are placed in correct envelopes is

Five gates labelled A, B, C, D & E, all having different décor outside are kept for VIP entries. Three different country delegates were invited and were taken inside through three different gates and while leaving it was made sure that they do not go out through the same gate from which they entered and also NOT from the same gate from which the other delegate is leaving. How many ways can the entry and exit arrangements be made?

How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?

A computer code consists of 2 non-zero numbers and 2 different alphabets, in that order. The condition for the code is that the alphabets position and the number taken should not be the same, for example, if the two numbers taken are 2 and 3 in that order, 2^nd, 3^rd and 23^rd alphabet cannot be taken but if number 32 is taken then only 3^rd and 2^nd alphabet will be excluded as there is no 32^nd alphabet. How many different combinations of the code are possible?

In how many ways is it possible to choose two black squares on an 8 × 8 chessboard so that they neither lie in the same row nor in the same column?

A boy needs to climb a staircase of 10 stairs. At each step he can cover either one stair or two stairs. The number of different ways in which he can climb the staircase is

There are 8 couples in a party, each couple having a husband and a wife. In an event at the party, husbands had to dance with wives. In how many ways can 4 husbands dance with their respective wives and the remaining four with women who are definitely not their wives?